In Final Fantasy XIII, you can upgrade and strengthen your accessories and weapons by crafting. The crafting system, accessed through save stations, allow you use to apply items to your accessories/weapons to increase their EXP multiplier and level them with EXP.

As you adventure and defeat enemies, you'll find yourself constantly receiving items with either a tooth symbol or bolt symbol next to them. These items are known as components, and they are the basis of the crafting system. Organic components, identified by the tooth symbol, are your basic materials. These offer low EXP, but they increase the EXP multiplier. The multiplier starts at x1, but will grow to x1.25, x1.5, x1.75, x2 and finally x3. Obviously, you'll gain the most benefit by getting the EXP multiplier to x3.The other type of component are synthetic componenets, identified by the bolt symbol. These are your advanced materials, and offer large EXP per use. The downside to synthetic materials is that using them will gradually decrease the EXP multiplier. Because of this, the best way to upgrade your gear is to get a x3 multiplier, then use synthetic components in bulk, so that they all benefit from the x3 multiplier. This way you can reach max level (indicated by this star symbol, ★) a lot easier.

Next, we have catalysts. These are materials that you can use on ★ equipment to transmute them into the next tier of equipment. Unlike the components, however, every accessory and weapon requires a specific catalyst in order to transmute them. For instance, transmuting an Adamantite Bangle to a Wurztite Bangle will require Dark Matter, whereas transmuting a Blazefire Saber to a Flamberge will require a Perovskite. These catalysts are typically hard to come by and relatively expensive to purchase, and are responsible for the majority of your Gil consumption in the game. Catalysts are identified by the gem/rock symbol next to the item.

Lastly, we have the Retail Networks that sell these components. Specifically, the stores that sell them are Creature Comforts (organic components), Lenora's Garage (synthetic components), The Motherlode (catalysts) and R&D Garage (high-level synthetic components and catalysts). The next section, 1.2: Upgrading Efficiently, will detail which components in particular are best for upgrading, and how to effectively use them.

In order to upgrade your accessories and weapons efficiently, not only do you have to take advantage of the 3x EXP multiplier and use synthetic components in bulk, you also need to use appropriate components. Because of the vast numbers of components that you'll actually need over the course of the game to properly upgrade everything, obtaining them through battle is highly inefficent, so the best course of action is to simply purchase everything.

There are only really three components you'll want to use throughout the game: Sturdy Bones, Superconductors and Ultracompact Reactors. These can all be bought and offer the greatest yield in regards to EXP per Gil spent. Sturdy Bones can be purchased from Creature Comforts as of Chapter 5, and cost 80 Gil. Superconductors can be purchased from Lenora's Garage as of Chapter 11, after visiting the Earthworks for the first time - they cost 840 Gil. Ultracompact Reactors can be purchased from R&D Depot, which unlocks upon completing Cie'th Stone Mission 07 - these cost 50,000 Gil.

Once you have access to these, you'll want to get to work on upgrading all your equipment efficiently. Using 36 Sturdy Bones will automatically push the EXP multiplier up to x3, so you should always do so before using synthetic components. Use the Superconductors or Ultracompact Reactors in bulk so that you can reach ★ without having to boost the EXP multiplier. Exact requirements for each component type can be found in 2.0 and 3.0. For details on farming Gil to be able to purchase the components and catalysts, please refer to my Final Fantasy XIII Farming Guide.

When upgrading accessories and weapons, you need to use a certain catalyst item to transmute an accessory or weapon to its next tier. These catalysts can be found in many different ways (detailed in 1.4 below), and here I will list how many of each catalyst you will require to upgrade every weapon and accessory:

Accessories:
Rhodochrosite x1
Cobaltite x1
Perovskite x22
Uraninite x6
Mnar Stone x1
Adamantite x2
Dark Matter x4
Weapons:
Cobaltite x3
Perovskite x15
Uraninite x14
Scarletite x12
Adamantite x3
Dark Matter x1
Trapezohedron x6
Overall:
Rhodochrosite x1
Cobaltite x4
Perovskite x37
Uraninite x20
Mnar Stone x1
Scarletite x12
Adamantite x5
Dark Matter x5
Trapezohedron x6

Given there are so many catalysts that are required, you'll obviously want to obtain as many as possible without having to purchase them. Below I'll list every guaranteed location for each catalyst, as well as drops for enemies that are viable for farming, along with store prices:

Rhodochrosite:
Cie'th Stone Mission 09
Cie'th Stone Mission 16
Cie'th Stone Mission 20
Cie'th Stone Mission 56
The Motherlode - 8,000 Gil
Cobaltite:
Cie'th Stone Mission 02
Cie'th Stone Mission 13
Cie'th Stone Mission 19
Cie'th Stone Mission 25
The Motherlode - 17,000 Gil
Perovskite:
The Motherlode - 30,000 Gil
Uraninite:
Havoc Skytank - Palom Polum (100% droprate)
Cie'th Stone Mission 29
Cie'th Stone Mission 30
Cie'th Stone Mission 36
Cie'th Stone Mission 57
The Motherlode - 45,000 Gil
Mnar Store:
Cie'th Stone Mission 47
Cie'th Stone Mission 60
The Motherlode - 60,000 Gil
Scarletite:
Sacrifice - Orphan's Cradle (5% droprate - you should easily get these if you farm the Sacrifices for Gil in Chapter 13)
Cie'th Stone Mission 50
The Motherlode - 100,000 Gil
Adamantite:
R&D Depot - 220,000 Gil
Dark Matter:
Shaolong Gui - Archylte Steppe (5% droprate)
R&D Depot - 840,000 Gil
Trapezohedron:
Adamantortoise - Archylte Steppe (1% droprate)
Adamantoise - Archylte Steppe/Eden (1% droprate)
Long Gui - Archylte Steppe (5% droprate)
R&D Depot - 2,000,000 Gil
Dismantling Tier 3 weaponry/Genji Gloves - please refer to 4.1: Obtaining six (6) Trapezohedrons without farming Oretoises for details

The purpose of this section is to demonstrate just how much Gil will be required to achieve Treasure Hunter, assuming you collect all the available Catalysts listed in 1.4: Catalyst Item Locations and do the majority of upgrading with Sturdy Bones, Superconductors and Ultracompact Reactors, as recommended in 1.2: Upgrading Efficently. This list will assume you obtain all Scarletites from Sacrifices, Dark Matters from Shaolong Guis and Trapezohedrons from Oretoises or dismantling. If you want to buy any of these, then please add extra to the total:

Catalysts:
Perovskite x37 - 1,110,000 Gil
Uraninite x15 - 600,000 Gil
Adamantite x5 - 1,100,000 Gil
Components (these numbers are based on you upgrading the chepeast weapon to Tier 3 for each Character - if you upgrade other weapons to Tier 3, it will cost more):
Sturdy Bones x5,368 - 430,880 Gil
Superconductors x1,555 - 1,306,200 Gil
Ultracompact Reactors x13 - 650,000 Gil
Trapezohedrons via Dismantling (see 4.1):
Sturdy Bones x144 - 11,520 Gil
Superconductors x39 - 32,760 Gil
Ultracompact Reactors x28 - 1,400,000 Gil
Grand Total:
Obtaining Trapezohedrons via Dismantling - 6,641,360 Gil
Obtaining Trapezohedrons via Farming - 5,197,080 Gil

Below is a list of every accessory that is required, along with how to obtain them, what they cost, EXP required to fully upgrade them, components to upgrade them and what catalysts are required. I have only included the latter three categories for accessories that you have to transmute to get a particular item - if you can receive the next tier of accessory by purchasing it or finding it throughout the game, then I won't list such details.

Here is how to read each description:

Name
Location: Where you'll find it in the game
Buy: Which Retail Network it can be purchased from, and for how much
EXP Required to Upgrade (★): Total EXP a base item will need to fully upgrade it to max level
Components Required: A list of cost-effective components in order to fully upgrade the item - components should be used from left to right, using the numbers indicated (eg x36) in one go
Components Cost: Overall cost of components if purchased from the Retail Networks
Catalyst: Catalyst material required to transmute item to next tier

2.1: HP Bangles

Iron Bangle
Location: The Hanging Edge - Aerorail Trussway 12-E
Buy: B&W Outfitters - 500 Gil

Silver Bangle
Location: Lake Bresha - Amid Timebound Waves
Buy: B&W Outfitters - 800 Gil

Tungsten Bangle
Location: Palumpolum - Felix Heights
Buy: B&W Outfitters - 1,500 Gil

Titanium Bangle
Buy: B&W Outfitters - 3,600 Gil

Gold Bangle
Location: The Palamecia - Bridge Access
Buy: B&W Outfitters - 9,000 Gil

Mythril Bangle
Location: Yaschas Massif - The Pass of Paddra
Buy: B&W Outfitters - 15,000 Gil

Platinum Bangle
Location: Mah'habara - Maw of Abyss
Buy: Sanctum Labs - 48,000 Gil

Diamond Bangle
Location: Cie'th Stone Mission 26

Adamant Bangle
Location: Orphan's Cradle - The Tesseracts
EXP Required to Upgrade (★): 331,065
Components Required: 36x Sturdy Bones, 4x Ultracompact Reactors
Components Cost: 202,880 Gil
Catalyst: Dark Matter

Wurtzite Bangle
Location: Transmute Adamant Bangle

2.2: Strength Wristbands

Power Wristband
Location: The Pulse Vestige - Ambulatory
Buy: B&W Outfitters - 1,000 Gil

Brawler's Wristband
Location: Palumpolum - The Estheim Residence
Buy: B&W Outfitters - 3,000 Gil

Warrior's Wristband
Location: Cie'th Stone Mission 23
Buy: B&W Outfitters - 10,000 Gil

Power Glove
Location: Eden - Edenhall
EXP Required to Upgrade (★): 58,960
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor
Components Cost: 52,880 Gil
Catalyst: Dark Matter

Kaiser Knuckles
Location: Transmute Power Glove

2.3: Magic Marks

Magician's Mark
Location: Lake Bresha - Amid Timebound Waves
Buy: B&W Outfitters - 1,000 Gil

Shaman's Mark
Location: Palumpolum - Rivera Towers
Buy: B&W Outfitters - 3,000 Gil

Sorcerer's Mark
Location: Cie'th Stone Mission 5
Buy: B&W Outfitters - 10,000 Gil

Weirding Glyph
Location: Orphan's Cradle - The Tesseracts
EXP Required to Upgrade (★): 58,960
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor
Components Cost: 52,880 Gil
Catalyst: Dark Matter

Magistral Crest
Location: Transmute Weirding Glyph

2.4: Armoured Accessories

Black Belt
Location: The Vile Peaks - Wrack and Ruin
Buy: B&W Outfitters - 4,500 Gil

General's Belt
Location: Cie'th Stone Mission 44
Buy: B&W Outfitters - 12,000 Gil
EXP Required to Upgrade (★): 27,420
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Adamantite

Champion's Belt
Location: Transmute General's Belt[/b]

Rune Bracelet
Location: The Palamecia - Bridge Access
Buy: B&W Outfitters - 4,500 Gil

Witch's Bracelet
Location: The Archylte Steppe
Buy: B&W Outfitters - 12,000 Gil
EXP Required to Upgrade (★): 27,420
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 19,320 Gil
Catalyst: Adamantite

Magus's Bracelet
Location: Transmute Witch's Bracelet

Royal Armlet
Location: The Palamecia - Cargo Access
Buy: Sanctum Labs - 200,000 Gil

Imperial Armlet
Location: Orphan's Cradle - The Tesseracts

2.5: Elemental Resist Rings

Ember Ring
Location: The Vile Peaks - Devastated Dreams

Blaze Ring
Location: Eden - Siren Park/Dismantle ★Fire Charm
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Salamandrine Ring
Location: Transmute Blaze Ring

Frost Ring
Location: Cie'th Stone Mission 11/Dismantle ★Ice Charm
EXP Required to Upgrade (★): 1,260
Components Required: 8x Sturdy Bones, 1x Superconductor
Components Cost: 1,480 Gil
Catalyst: Cobaltite

Icicle Ring
Location: Transmute Frost Ring
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Boreal Ring
Location: Transmute Icicle Ring

Spark Ring
Location: Lake Bresha - Forgotten Commons/Dismantle ★Lightning Charm

Fulmen Ring
Location: Cie'th Stone Mission 6
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Raijin Ring
Location: Transmute Fulmen Ring

Aqua Ring
Location: The Sunleth Waterscape - Rain-spotted Veil/Dismantle ★Water Charm

Riptide Ring
Location: Sulyya Springs - Subterranean Lake
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Nereid Ring
Location: Transmute Riptide Ring

Zephyr Ring
Location: The Archylte Steppe/Dismantle ★Wind Charm

Gale Ring
Location: Taejin's Tower - Fourth Tier
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Sylphid Ring
Location: Transmute Blaze Ring

Clay Ring
Location: The Archylte Steppe/Dismantle ★Earth Charm

Siltstone Ring
Location: Cie'th Stone Mission 39
EXP Required to Upgrade (★): 3,620
Components Required: 20x Sturdy Bones, 3x Superconductors
Components Cost: 4,120 Gil
Catalyst: Uraninite

Gaian Ring
Location: Transmute Siltstone Ring

2.6: Status Resist Items

Giant's Glove
Location: Cie'th Stone Mission 28
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Warlord's Glove
Location: Transmute Giant's Glove

Glass Buckle
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Tektike Buckle
Location: Transmute Glass Buckle

Metal Armband
Location: The Vile Peaks - Munitions Necropolis
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Ceramic Armband
Location: Transmute Metal Armband

Serenity Sachet
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Safeguard Sachet
Location: Transmute Serenity Sachet

Glass Orb
Location: Taejin's Tower - Fourth Tier
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Dragonfly Orb
Location: Transmute Glass Orb

Star Pendant
Location: The Gapra Whitewood - Field Trial Range S
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Starfall Pendant
Location: Transmute Star Pendant

Pearl Necklace
Location: Cie'th Stone Mission 4
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Gemstone Necklace
Location: Transmute Pearl Necklace

Warding Talisman
Location: Palumpolum - Nutriculture Complex
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Hexbane Talisman
Location: Transmute Warding Talisman

Pain Dampener
Location: The Palamecia - Rotary Shaft
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Pain Deflector
Location: Transmute Pain Dampener

White Cape
Location: The Palamecia - Rotary Shaft
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Effulgent Cape
Location: Transmute White Cape

Rainbow Anklet
Location: The Fifth Ark - Lower Traverse
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Moonbow Anklet
Location: Transmute Rainbow Anklet

Cherub's Crown
Location: Orphan's Cradle - The Tesseracts
Buy: B&W Outfitters - 3,000 Gil
EXP Required to Upgrade (★): 3,390
Components Required: 16x Sturdy Bones, 3x Superconductors
Components Cost: 3,800 Gil
Catalyst: Perovskite

Seraph's Crown
Location: Transmute Cherub's Crown

2.7: Status Provide Items

Guardian Amulet
Location: Palumpolum - Central Arcade
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Shield Talisman
Location: Transmute Guardian Amulet

Auric Amulet
Location: The Vile Peaks - Scrap Processing
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Soulfont Talisman
Location: Transmute Auric Amulet

Watchman's Amulet
Location: The Gapra Whitewood - Environmental Regulation
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Shrouding Talisman
Location: Transmute Watchman's Amulet

Hero's Amulet
Location: The Fifth Ark - Vestibular Hold
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Morale Talisman
Location: Transmute Hero's Amulet

Saint's Amulet
Location: The Fifth Ark - Lower Traverse
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Blessed Talisman
Location: Transmute Saint's Amulet

Zealot's Amulet
Location: The Faultwarrens - Via Lunae (Titan Quest C-1)
Buy: Magical Moments - 5,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Battle Talisman
Location: Transmute Zealot's Amulet

Flamebane Brooch
Location: Oerba - Rust-eaten Bridge
Buy: Magical Moments - 3,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Flameshield Earring
Location: Transmute Flamebane Brooch

Frostbane Brooch
Location: Taejin's Tower - The Cloven Spire
Buy: Magical Moments - 3,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Frostshield Earring
Location: Transmute Frostbane Brooch

Sparkbane Brooch
Location: Taejin's Tower - Ground Tier
Buy: Magical Moments - 3,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Sparkshield Earring
Location: Transmute Sparkbane Brooch

Aquabane Brooch
Location: Sulyya Springs - Subterranean Lake
Buy: Magical Moments - 3,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Aquashield Earring
Location: Transmute Aquabane Brooch

Hermes Sandals
Location: Cie'th Stone Mission 34
Buy: Magical Moments - 3,000 Gil
EXP Required to Upgrade (★): 600
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Perovskite

Sprint Shoes
Location: Transmute Hermes Sandals

Tetradic Crown
Location: Orphan's Cradle - The Tesseracts

Tetradic Tiara
Location: Archylte Steppe - Chocobo 10th Treasure/Dahaka - Taejin's Tower (100% droprate)

2.8: Movement Accessories

Whistlewind Scarf
Location: The Palamecia - Starboard Weather Deck
Buy: Moogleworks - 1,000 Gil
EXP Required to Upgrade (★): 350
Components Required: 1x Superconductor
Components Cost: 840 Gil
Catalyst: Rhodochrosite

Aurora Scarf
Location: Transmute Whistlewind Scarf

Nimbletoe Boots
Buy: Moogleworks - 6,000 Gil

2.9: Battle Accessories

Gold Watch
Location: Cie'th Stone Mission 64

Champion's Badge
Location: Eden - Siren Park

Survivalist Catalog
Location: Cie'th Stone Mission 15

Collector's Catalog
Location: Taejin's Tower - Seventh Tier/Cie'th Stone Mission 08
Buy: Moogleworks - 100,000 Gil
EXP Required to Upgrade (★): 1,050
Components Required: 8x Sturdy Bones, 2x Superconductors
Components Cost: 2,320 Gil
Catalyst: Mnar Stone

Connoisseur Catalog
Location: Transmute Collector's Catalog

2.10: Kill Bonus Accessories

Hunter's Friend
Location: Cie'th Stone Mission 45

Speed Sash
Location: The Archylte Steppe
Buy: Moogleworks - 10,000 Gil

Energy Sash
Location: Cie'th Stone Mission 1

2.11: Miscellaneous Accessories

Doctor's Code
Location: The Sunleth Waterscape - Sun-dappled Trail

Growth Egg
Location: Cie'th Stone Mission 55

Entite Ring
Location: Archylte Steppe - Chocobo 15th Treasure
Buy: Sanctum Labs - 120,000 Gil

Goddess's Favor
Location: Oerba - Rust-eaten Bridge

Ribbon
Location: Archylte Steppe - Chocobo 20th Treasure
EXP Required to Upgrade (★): 20,430
Components Required: 36x Sturdy Bones, 24x Superconductors
Components Cost: 23,040 Gil
Catalyst: Dark Matter

Super Ribbon
Location: Transmute Ribbon

Genji Glove
Location: Cie'th Stone Missions 51, 62, 63

2.12: Elemental Eaters

Fire Charm
Location: Archylte Steppe

Ice Charm
Location: Archylte Steppe

Lightning Charm
Location: Archylte Steppe

Water Charm
Location: Sulyya Springs - Subterranean Lake

Wind Charm
Location: Archylte Steppe

Earth Charm
Location: Archylte Steppe

Twenty-sided Die
Location: Cie'th Stone Mission 48

Below is a list of every weapon that is required, along with how to obtain them, what they cost, EXP required to fully upgrade them, components to upgrade them and what catalysts are required. Do note that for the Tier 3 weapons (Omega Weapon, Total Eclipses, Save the Queen, Nue, Nirvana and Kain's Lance), you only have to obtain one variant of the eight possible versions.

Here is how to read each description:

Name
Location: Where you'll find it in the game
Buy: Which Retail Network it can be purchased from, and for how much
EXP Required to Upgrade (★): Total EXP a base item will need to fully upgrade it to max level
Components Required: A list of cost-effective components in order to fully upgrade the item - components should be used from left to right, using the numbers indicated (eg x36) in one go
Components Cost: Overall cost of components if purchased from the Retail Networks
Catalyst: Catalyst material required to transmute item to next tier

3.1: Lightning's Gunblades

Blazefire Saber
Buy: Up In Arms - 2,000 Gil
EXP Required to Upgrade (★): 24,600
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 23,040 Gil
Catalyst: Perovskite

Flamberge
Location: Transmute Blazfire Saber
EXP Required to Upgrade (★): 449,310
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 36x Superconductors
Components Cost: 186,000 Gil
Catalyst: Trapezohedron

Omega Weapon (Flamberge)
Location: Transmute Flamberge


Axis Blade
Buy: Plautus's Workshop - 15,000 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 46x Superconductors
Components Cost: 41,520 Gil
Catalyst: Adamantite

Enkindler
Location: Transmute Axis Blade
EXP Required to Upgrade (★): 287,154
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 42x Superconductors
Components Cost: 191,040 Gil
Catalyst: Trapezohedron

Omega Weapon (Enkindler)
Location: Transmute Enkindler


Edged Carbine
Buy: Up In Arms - 4,600 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 26,400 Gil
Catalyst: Perovskite

Razor Carbine
Location: Transmute Edged Carbine
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron

Omega Weapon (Razor Carbine)
Location: Transmute Razor Carbine


Lifesaber
Buy: Plautus's Workshop - 20,000 Gil
EXP Required to Upgrade (★): 70,850
Components Required: 36x Sturdy Bones, 50x Superconductors
Components Cost: 44,880 Gil
Catalyst: Scarletite

Peacemaker
Location: Transmute Lifesaber
EXP Required to Upgrade (★): 237,000
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 43x Superconductors
Components Cost: 141,880 Gil
Catalyst: Trapezohedron

Omega Weapon (Peacemaker)
Location: Transmute Peacemaker


Gladius
Buy: Up In Arms - 7,100 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Helter-Skelter
Location: Transmute Gladius
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Omega Weapon (Helter-Skelter)
Location: Transmute Helter-Skelter


Organyx
Buy: Gilgamesh, Inc. - 280,000 Gil
EXP Required to Upgrade (★): 20,100
Components Required: 36x Sturdy Bones, 9x Superconductors
Components Cost: 10,440 Gil
Catalyst: Cobaltite

Apocalypse
Location: Transmute Organyx
EXP Required to Upgrade (★): 233,872
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors
Components Cost: 102,880 Gil
Catalyst: Trapezohedron

Omega Weapon (Apocalypse)
Location: Transmute Apocalypse


Hauteclaire
Buy: Gilgamesh, Inc. - 20,000 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Durandal
Location: Transmute Hauteclaire
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Omega Weapon (Durandal)
Location: Transmute Durandal


Lionheart
Buy: Plautus's Workshop - 28,000 Gil
EXP Required to Upgrade (★): 63,060
Components Required: 36x Sturdy Bones, 53x Superconductors
Components Cost: 46,560 Gil
Catalyst: Scarletite

Ultima Weapon
Location: Transmute Lionheart
EXP Required to Upgrade (★): 227,448
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 37x Superconductors
Components Cost: 186,840 Gil
Catalyst: Trapezohedron

Omega Weapon (Ultima Weapon)
Location: Transmute Ultima Weapon

3.2: Sazh's Pistols

Vega 42s
Buy: Up In Arms - 2,000 Gil
EXP Required to Upgrade (★): 24,600
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 23,040 Gil
Catalyst: Perovskite

Altairs
Location: Transmute Vega 42s
EXP Required to Upgrade (★): 449,310
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 36x Superconductors
Components Cost: 186,000 Gil
Catalyst: Trapezohedron

Total Eclipses (Altairs)
Location: Transmute Altairs


Spica Defenders
Buy: Plautus's Workshop - 14,500 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 46x Superconductors
Components Cost: 41,520 Gil
Catalyst: Scarletite

Serius Sidearms
Location: Transmute Spica Defenders
EXP Required to Upgrade (★): 221,600
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 31x Superconductors
Components Cost: 131,800 Gil
Catalyst: Trapezohedron

Total Eclipses (Serius Sidearms)
Location: Transmute Serius Sidearms


Deneb Duellers
Buy: Up In Arms - 3,900 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 26,400 Gil
Catalyst: Perovskite

Canopus AMPs
Location: Transmute Deneb Duellers
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 28x Superconductors
Components Cost: 179,280 Gil
Catalyst: Trapezohedron

Total Eclipses (Canopus AMPs)
Location: Transmute Canopus AMPs


Rigels
Buy: Gilgamesh, Inc. - 19,000 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Polaris Specials
Location: Transmute Rigels
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Total Eclipses (Polaris Specials)
Location: Transmute Polaris Specials


Aldebarans
Buy: Gilgamesh, Inc. - 263,000 Gil
EXP Required to Upgrade (★): 20,100
Components Required: 36x Sturdy Bones, 10x Superconductors
Components Cost: 11,280 Gil
Catalyst: Cobaltite

Sadalmeliks
Location: Transmute Aldebarans
EXP Required to Upgrade (★): 233,872
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 54x Superconductors
Components Cost: 101,120 Gil
Catalyst: Trapezohedron

Total Eclipses (Sadalmeliks)
Location: Transmute Sadalmeliks


Pleiades Hi-Powers
Buy: Gilgamesh, Inc. - 22,000 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 17,160 Gil
Catalyst: Perovskite

Hyades Magnums
Location: Transmute Pleiades Hi-Powers
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron


Total Eclipses (Hyades Magnums)
Location: Transmute Hyades Magnums

Antares Deluxes
Buy: Plautus's Workshop - 22,000 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Fomalhault Elites
Location: Transmute Antares Deluxes
EXP Required to Upgrade (★): 154,752
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 29x Superconductors
Components Cost: 80,120 Gil
Catalyst: Trapezohedron

Total Eclipses (Fomalhault Elites)
Location: Transmute Fomalhault Elites


Procyons
Buy: Plautus's Workshop - 30,000 Gil
EXP Required to Upgrade (★): 63,060
Components Required: 36x Sturdy Bones, 53x Superconductors
Components Cost: 46,560 Gil
Catalyst: Dark Matter

Betelgeuse Customs
Location: Transmute Procyons
EXP Required to Upgrade (★): 246,740
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 43x Superconductors
Components Cost: 191,880 Gil
Catalyst: Trapezohedron

Total Eclipses (Betelgeuse Customs)
Location: Transmute Betelgeuse Customs

3.3: Snow's Emblems

Wild Bear
Buy: Up In Arms - 1,800 Gil
EXP Required to Upgrade (★): 24,600
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 23,040 Gil
Catalyst: Perovskite

Feral Pride
Location: Transmute Wild Bear
EXP Required to Upgrade (★): 449,310
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 36x Superconductors
Components Cost: 186,000 Gil
Catalyst: Trapezohedron

Save the Queen (Feral Pride)
Location: Transmute Feral Pride


Paladin
Buy: Plautus's Workshop - 20,000 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 46x Superconductors
Components Cost: 41,520 Gil
Catalyst: Scarletite

Winged Saint
Location: Transmute Paladin
EXP Required to Upgrade (★): 221,600
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 31x Superconductors
Components Cost: 131,800 Gil
Catalyst: Trapezohedron

Save the Queen (Winged Saint)
Location: Transmute Winged Saint


Rebel Heart
Buy: Plautus's Workshop - 11,000 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Warrior's Emblem
Location: Transmute Rebel Heart
EXP Required to Upgrade (★): 154,752
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 29x Superconductors
Components Cost: 80,120 Gil
Catalyst: Trapezohedron

Save the Queen (Warrior's Emblem)
Location: Transmute Warrior's Emblem


Power Circle
Buy: Up In Arms - 4,500 Gil
EXP Required to Upgrade (★): 89,700
Components Required: 36x Sturdy Bones, 75x Superconductors
Components Cost: 65,880 Gil
Catalyst: Scarletite

Battle Standard
Location: Transmute Power Circle
EXP Required to Upgrade (★): 477,568
Components Required: 36x Sturdy Bones, 5x Ultracompact Reactors
Components Cost: 252,880 Gil
Catalyst: Trapezohedron

Save the Queen (Battle Standard)
Location: Transmute Battle Standard


Feymark
Buy: Gilgamesh, Inc. - 25,000 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Soul Blazer
Location: Transmute Feymark
EXP Required to Upgrade (★): 154,752
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 30x Superconductors
Components Cost: 80,960 Gil
Catalyst: Trapezohedron

Save the Queen (Soul Blazer)
Location: Transmute Soul Blazer


Sacrifical Circle
Buy: Gilgamesh, Inc. - 210,000 Gil
EXP Required to Upgrade (★): 89,700
Components Required: 36x Sturdy Bones, 75x Superconductors
Components Cost: 65,880 Gil
Catalyst: Scarletite

Indomitus
Location: Transmute Sacrificial Circle
EXP Required to Upgrade (★): 477,568
Components Required: 36x Sturdy Bones, 5x Ultracompact Reactors
Components Cost: 252,880 Gil
Catalyst: Trapezohedron

Save the Queen (Indomitus)
Location: Transmute Indomitus


Unsettling Sun
Buy: Plautus's Workshop - 21,000 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 17,160 Gil
Catalyst: Perovskite

Midnight Sun
Location: Transmute Unsettling Sun
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 29x Superconductors
Components Cost: 180,120 Gil
Catalyst: Trapezohedron

Save the Queen (Midnight Sun)
Location: Transmute Midnight Sun


Umbra
Buy: Plautus's Workshop - 32,600 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 47x Superconductors
Components Cost: 42,360 Gil
Catalyst: Adamantite

Solaris
Location: Transmute Umbra
EXP Required to Upgrade (★): 287,154
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 42x Superconductors
Components Cost: 191,040 Gil
Catalyst: Trapezohedron

Save the Queen (Solaris)
Location: Transmute Solaris

3.4: Hope's Boomerangs

Airwing
Buy: Plautus's Workshop - 10,000 Gil
EXP Required to Upgrade (★): 22,440
Components Required: 36x Sturdy Bones, 14x Superconductors
Components Cost: 23,880 Gil
Catalyst: Uraninite

Skycutter
Location: Transmute Airwing
EXP Required to Upgrade (★): 171,492
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 46x Superconductors
Components Cost: 94,400 Gil
Catalyst: Trapezohedron

Nue (Skycutter)
Location: Transmute Skycutter


Hawkeye
Buy: Up In Arms - 4,400 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 18,000 Gil
Catalyst: Perovskite

Eagletalon
Location: Transmute Hawkeye
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron

Nue (Eagletalon)
Location: Transmute Eagletalon


Otshirvani
Buy: Plautus's Workshop - 28,200 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 47x Superconductors
Components Cost: 42,360 Gil
Catalyst: Scarletite

Urubutsin
Location: Transmute Otshirvani
EXP Required to Upgrade (★): 221,600
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 32x Superconductors
Components Cost: 132,640 Gil
Catalyst: Trapezohedron

Nue (Urubutsin)
Location: Transmute Urubutsin


Ninurta
Buy: Up In Arms - 2,800 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 18,000 Gil
Catalyst: Perovskite

Jataya
Location: Transmute Ninurta
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron

Nue (Jataya)
Location: Transmute Jataya


Vidofnir
Buy: Plautus's Workshop - 16,900 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 47x Superconductors
Components Cost: 42,360 Gil
Catalyst: Scarletite

Hresvelgr
Location: Transmute Vidofnir
EXP Required to Upgrade (★): 221,600
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 32x Superconductors
Components Cost: 132,640 Gil
Catalyst: Trapezohedron

Nue (Hresvelgr)
Location: Transmute Hresvelgr


Simurgh
Buy: Gilgamesh, Inc. - 21,200 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Tezcatlipoca
Location: Transmute Simurgh
EXP Required to Upgrade (★): 154,752
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, x29 Superconductors
Components Cost: 80,120 Gil
Catalyst: Trapezohedron

Nue (Tezcatlipoca)
Location: Transmute Tezcatlipoca


Malphas
Buy: Gilgamesh, Inc. - 198,000 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 17,160 Gil
Catalyst: Perovskite

Naberius
Location: Transmute Malphas
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron

Nue (Naberius)
Location: Transmute Naberius


Alicanto
Buy: Gilgamesh, Inc. - 18,000 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Caladrius
Location: Transmute Alicanto
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Nue (Caladrius)
Location: Transmute Caladrius

3.5: Vanille's Rods

Binding Rod
Buy: Up In Arms - 2,500 Gil
EXP Required to Upgrade (★): 24,600
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 23,040 Gil
Catalyst: Perovskite

Hunter's Rod
Location: Transmute Binding Rod
EXP Required to Upgrade (★): 445,950
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 35x Superconductors
Components Cost: 185,160 Gil
Catalyst: Trapezohedron

Nirvana (Hunter's Rod)
Location: Transmute Hunter's Rod


Tigerclaw
Buy: Gilgamesh, Inc. - 300,000 Gil
EXP Required to Upgrade (★): 44,760
Components Required: 36x Sturdy Bones, 21x Superconductors
Components Cost: 20,520 Gil
Catalyst: Cobaltite

Wyrmfang
Location: Transmute Tigerclaw
EXP Required to Upgrade (★): 233,872
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors
Components Cost: 102,880 Gil
Catalyst: Trapezohedron

Nirvana (Wyrmfang)
Location: Transmute Wyrmfang


Healer's Staff
Buy: Plautus's Workshop - 19,800 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 47x Superconductors
Components Cost: 42,360 Gil
Catalyst: Adamantite

Physician's Staff
Location: Transmute Healer's Staff
EXP Required to Upgrade (★): 281,160
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 35x Superconductors
Components Cost: 185,160 Gil
Catalyst: Trapezohedron

Nirvana (Physician's Staff)
Location: Transmute Physician's Staff


Pearlwing Staff
Buy: Up In Arms - 2,300 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 18,000 Gil
Catalyst: Perovskite

Brightwing Staff
Location: Transmute Pearlwing Staff
EXP Required to Upgrade (★): 438,360
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 30x Superconductors
Components Cost: 180,960 Gil
Catalyst: Trapezohedron

Nirvana (Brightwing Staff)
Location: Transmute Brightwing Staff


Rod of Thorns
Buy: Up In Arms - 3,000 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 18,000 Gil
Catalyst: Perovskite

Orochi Rod
Location: Transmute Rod of Thorns
EXP Required to Upgrade (★): 470,550
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 52x Superconductors
Components Cost: 199,440 Gil
Catalyst: Trapezohedron

Nirvana (Orochi Rod)
Location: Transmute Orochi Rod


Mistilteinn
Buy: Plautus's Workshop - 11,000 Gil
EXP Required to Upgrade (★): 66,750
Components Required: 36x Sturdy Bones, 47x Superconductors
Components Cost: 42,360 Gil
Catalyst: Scarletite

Erinye's Cane
Location: Transmute Mistilteinn
EXP Required to Upgrade (★): 218,210
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, x27 Superconductors
Components Cost: 128,440 Gil
Catalyst: Trapezohedron

Nirvana (Erinye's Cane)
Location: Transmute Erinye's Cane


Belladonna Wand
Buy: Plautus's Workshop - 31,200 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Malboro Wand
Location: Transmute Belladonna Wand
EXP Required to Upgrade (★): 153,000
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 28x Superconductors
Components Cost: 79,280 Gil
Catalyst: Trapezohedron

Nirvana (Malboro Wand)
Location: Transmute Malboro Wand


Heavenly Axis
Buy: Gilgamesh, Inc. - 24,000 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Abraxas
Location: Transmute Alicanto
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Nirvana (Abraxas)
Location: Transmute Abraxas

3.6: Fang's Spears

Bladed Lance
Buy: Up In Arms - 4,500 Gil
EXP Required to Upgrade (★): 24,600
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 23,040 Gil
Catalyst: Perovskite

Glaive
Location: Transmute Bladed Lance
EXP Required to Upgrade (★): 445,950
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors, 36x Sturdy Bones, 35x Superconductors
Components Cost: 185,160 Gil
Catalyst: Trapezohedron

Kain's Lance (Glaive)
Location: Transmute Glaive


Dragoon Lance
Buy: Gilgamesh, Inc. - 230,000 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Dragonhorn
Location: Transmute Dragoon Lance
EXP Required to Upgrade (★): 152,640
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 27x Superconductors
Components Cost: 128,440 Gil
Catalyst: Trapezohedron

Kain's Lance (Dragonhorn)
Location: Transmute Dragonhorn


Partisan
Buy: Up In Arms - 6,600 Gil
EXP Required to Upgrade (★): 33,000
Components Required: 36x Sturdy Bones, 17x Superconductors
Components Cost: 18,000 Gil
Catalyst: Perovskite

Rhomphaia
Location: Transmute Partisan
EXP Required to Upgrade (★): 274,350
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 7x Superconductors
Components Cost: 111,640 Gil
Catalyst: Trapezohedron

Kain's Lance (Rhomphaia)
Location: Transmute Rhomphaia


Shamanic Spear
Buy: Gilgamesh, Inc. - 23,000 Gil
EXP Required to Upgrade (★): 38,040
Components Required: 36x Sturdy Bones, 23x Superconductors
Components Cost: 22,200 Gil
Catalyst: Uraninite

Heretic's Halberd
Location: Transmute Shamanic Spear
EXP Required to Upgrade (★): 153,000
Components Required: 36x Sturdy Bones, 1x Ultracompact Reactor, 36x Sturdy Bones, 28x Superconductors
Components Cost: 79,280 Gil
Catalyst: Trapezohedron

Kain's Lance (Heretic's Halberd)
Location: Transmute Heretic's Halberd


Punisher
Buy: Plautus's Workshop - 31,000 Gil
EXP Required to Upgrade (★): 70,850
Components Required: 36x Sturdy Bones, 50x Superconductors
Components Cost: 44,880 Gil
Catalyst: Scarletite

Banescissor Spear
Location: Transmute Punisher
EXP Required to Upgrade (★): 236,350
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 46x Superconductors
Components Cost: 144,400 Gil
Catalyst: Trapezohedron

Kain's Lance (Banescissor Spear)
Location: Transmute Banescissor Spear


Pandoran Spear
Buy: Plautus's Workshop - 16,200 Gil
EXP Required to Upgrade (★): 70,850
Components Required: 36x Sturdy Bones, 50x Superconductors
Components Cost: 44,880 Gil
Catalyst: Scarletite

Calamity Spear
Location: Transmute Pandoran Spear
EXP Required to Upgrade (★): 236,350
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 46x Superconductors
Components Cost: 144,400 Gil
Catalyst: Trapezohedron

Kain's Lance (Calamity Spear)
Location: Transmute Calamity Spear


Taming Pole
Buy: Gilgamesh, Inc. - 27,000 Gil
EXP Required to Upgrade (★): 54,800
Components Required: 36x Sturdy Bones, 33x Superconductors
Components Cost: 30,600 Gil
Catalyst: Uraninite

Venus Gospel
Location: Transmute Taming Pole
EXP Required to Upgrade (★): 334,656
Components Required: 36x Sturdy Bones, 3x Ultracompact Reactors
Components Cost: 152,880 Gil
Catalyst: Trapezohedron

Kain's Lance (Venus Gospel)
Location: Transmute Venus Gospel


Gae Bolg
Buy: Plautus's Workshop - 13,100 Gil
EXP Required to Upgrade (★): 70,850
Components Required: 36x Sturdy Bones, 50x Superconductors
Components Cost: 44,880 Gil
Catalyst: Scarletite

Gungnir
Location: Transmute Gae Bolg
EXP Required to Upgrade (★): 214,110
Components Required: 36x Sturdy Bones, 2x Ultracompact Reactors, 36x Sturdy Bones, 23x Superconductors
Components Cost: 125,080 Gil
Catalyst: Trapezohedron

Kain's Lance (Gungnir)
Location: Transmute Gungnir

4.1: Obtaining six (6) Trapezohedrons without farming Oretoises

In order to obtain the six Tier 3 weapons, you need to acquire a Trapezohedron for each of the upgrades. Normally this requires you to farm Adamantoises, Adamantortoises or Long Guis for hours in hope of getting them to drop. This is a long and tedious process, but thankfully, it can be bypassed. There is a way to obtain all six Trapezohedrons without farming a single Oretoise. This all comes down to dismantling Genji Gloves and a Nirvana (Malboro Wand).

The Genji Glove is an accessory obtainable from three of the Cie'th Stone Missions (51, 62 and 63) that allows your character's attack to exceed 99,999 damage. These are absolutely vital in defeating enemies such as Long Guis and Shaolong Guis, but they do have another purpose. When a fully upgraded Genji Glove (11,250 Experience to ★) is dismantled, you will receive a Trapezohedron. This means you can get three Trapezohedrons with little effort.

Now onto why the Nirvana (Malboro Wand) is helpful for this. When a fully upgraded Nirvana (Malboro Wand) (1,673,328 Experience to ★) is dismantled, you will receive THREE Trapezohedrons. Combined with the Trapezohedrons you got from dismantling the Genji Gloves, you'll have enough Trapezohedrons to make all the necessary Tier 3 weapons and get the trophy. The major problem with this method is that it requires dismantling your best accessories and best weapon, as well as fork out over 1 million Gil in upgrading the Nirvana to max level, so therefore it is highly recommended you do this after obtaining every other accessory and weapon, so that you can save beforehand and simply reload your save after receiving the trophy.

Below, I'll show step-by-step how to go about this process. As a reminder, you shouldn't do this until you've obtained every other accessory and weapon, and you should save beforehand so that you can reload afterwards:
Obtain three Genji Gloves by completing Cie'th Stone Missions 51, 62 and 63.
Upgrade all three Genji Gloves to ★ (requires 11,250 Experience).
Components Required: 36x Sturdy Bones, 13x Superconductors
Components Cost: 13,800 Gil
Dismantle all three Genji Gloves to obtain three Trapezohedrons.
Upgrade a Belladonna Wand to Malboro Wand, and Malboro Wand to Nirvana (Malboro Wand) using one of the three Trapezohedrons - refer to the weapon under Vanille's Rods for exact component and gil requirements (if you already have a maxed Malboro Wand, then you can ignore this).
Upgrade the Nirvana (Malboro Wand) to ★ (requires 1,673,328 Experience) - if you don't have enough gil for the 28 Ultracompact Reactors, feel free to sell your items to make up the loss, as you'll get them back after reloading.
Components Required: 36x Sturdy Bones, 28x Ultracompact Reactors
Components Cost: 1,402,880 Gil
Dismantle the Nirvana (Malboro Wand) to obtain three Trapezohedrons.
Make the other five Tier 3 weapons: Omega Weapon, Total Eclipses, Save the Queen, Nue, Kain's Lance.
Head to Oerba Village and talk to Bhakti to receive Treasure Hunter.
Reload your save to keep your weapon, accessories and gil.
With that, you've bypassed the biggest grind in Final Fantasy XIII! The only real downside to this method is that you won't be able to benefit from Tier 3 weapons in battle at all, but they're not all that necessary for any of the battles anyway.

4.2: Frequently Asked Questions

Q: Do you need to hold every accessory and weapon at once for Treasure Hunter?
A: No, simply picking up an item registers it for the trophy. However it is recommended you avoid selling anything until you know you have or can obtain every accessory and weapon. This mostly pertains to the Aqua Ring and Spark Ring, as they can only be obtained in earlier Chapters or by dismantling ★Charms.

Q: Do I need every version of the Tier 3 weapons?
A: No, one version for each character is sufficient.

Q: Which weapons should I upgrade to Tier 3?
A: The best route to go for reaching Tier 3 weapons is to simply upgrade the cheapest weapons. These weapons are:
Lightning: Organyx
Sazh: Antares Deluxes
Snow: Rebel Heart
Hope: Simurgh
Vanille: Belladonna Wand
Fang: Heretic's Halberd
Q: I can't access a certain store/item! How do I get them?
A: Sturdy Bones are accessible from Creature Comforts as of Chapter 5. Superconductors are accessible from Lenora's Garage as of Chapter 11, after visiting the Earthworks for the first time. Ultracompact Reactors are accessible from R&D Depot, which requires you to finish Cie'th Stone Mission 07.

Q: Should I farm Trapezohedrons, or get them by dismantling my gear?
A: I personally recommend the latter, as it saves a great deal of time. The one downside to this, however, is that you won't be able to use your Tier 3 weaponry at all.

Q: I've collected every accessory and weapon, but the trophy hasn't unlocked! What do I do?
A: In order to actually earn the trophy, you must first talk to Bhakti in Oerba Village. Once you do so, you'll receive the trophy.