Here is what the build looks like if you don't care about reading stuff.



Firstly put a point into Kinetic Aspis so we can actually do stuff in the tree. Our First Tree is Xiphos.



I put 5 points into "Gun Kata". It boosts Gun damage by 15% and melee damage by 50%. You will only get the melee damage buff if you have shot an enemy, but the build will make it work.
To the right is "Clarity of Purpose" which boosts melee damage by 25% and increases max health by 15%. Put 5 points into "Clarity of Purpose".
After that we put 5 points into "Mercurial". It is a kill skill that boosts movement speed and damage resistance by 20%. This is very usefull since enemies will try to run away from you when you get too close. If you get a kill with a gun, you can chase them with the movement speed and will take less damage on the way there AND you will do more melee damage once you get there thanks to "Gun Kata".
A lot of people put points into "Omega-Senshu". You can if you want to, but I don't put any points into it since I am generally powerful enough to kill an enemy in one hit. Also, it only does extra damage to enemies with less than 50% of their health, which does not include shields. If you are playing in Ultimate Vault Hunter Mode, enemies have more shield than health so by the time "Omega-Senshu" kicks in you have dealth with the enemy. It can be used to fight bosses and badasses and even non-shield enemies like Iwajira.
Instead, I put the 5 points into "Bloodlust". This skill allows you to heal 4% of your health every second for each enemy that is bleeding. After "Miss Moxxi's Probe" got nerfed, self healing became more difficult so this is just to help survivability.
The next point goes into "Rend". When you melee an enemy they bleed. It does extra damage to enemies with high health too. To make the Setup work, we Need to have "Rend" so do not skip it.
The Final skill we pick up is the capstone skill, Blood Rush. When you go to melee an enemy, you will dash toward them and deal 100% extra melee damage. It has a 10 second cooldown, but if you apply the bleed effect from "Rend" it instantly comes back. It also instantly comes back if you kill the enemy you Blood Rushed. This skill is extremely handy to have. You can dash faster than sprinting to individual enemies, deal increased melee damage to them, apply a bleed to them, and then dash to another enemy. If you have low health you can use "Blood Rush" to apply bleed to as many enemies as you can to get lots of health back. You can also clear rooms incredibly fast and deal more dps than Nisha!

So to recap:
5 Points in Gun Kata
5 Points in Clarity of Purpose
5 Points in Mercurial
1 Point in Rend
5 Points in BloodLust
1 Point in Blood Rush

You Should have 25 points remaining for the next tree.

The next skilltree to work on is "Phalanx"

My one looks like this:



Firstly, put 5 points into "Ephodos". This boosts movement speed and gun damage by 20% while holding the Aspis. The movement is the primary reason we pick up this skill.
Then we go straight to the second line and put 5 points into "Vanguard". Since it never hurts to be safe on health, this skill gives health regeneration to yourself and players around you depending on how much damage the Aspis has absorbed. If you play with friends, they will love you (maybe).
Afterwards, put 5 points in "Hold the Line". It will extend the time you hold the aspis by 5.5 seconds which allows you to absorb more damage and heal for more. It sounds dull, but it pays well.
Now 1 point into Prismatic Aegis. It is a great skill. Your aspis absorbs the element of whatever you were damaged by and when you throw it, the elements absorbed are used to damage the enemy hit. You can throw grenades at your feet while holding the Aspis and it will absorb that element. It is a great skill to have and only 1 point. Pick. It. Up.
Now, the 4th line in the tree. Ignore those skills. "United Front" restores your shield when your Aspis absorbs damage and increases its maximum capacity. We do not want any of those qualities. We are using a roid damage shield. We want it to be empty.
"Stalwart" increases your maximum health and allows teammates to shoot your Aspis to charge it up. If you play alone it is a useless skill and we already have a health buff from "Clarity of Purpose".
"Clear!" is an option since we will have leftover points. It allows you to revive downed teammates when you throw your Aspis at them and increases your damage by 40% while you are in fight for your life. For now, skip it.
I put 5 points into "Return Fire". The Aspis now has a 50% chance to reflect lasers and bullets at enemies and will still get charged from them. I like this skill. You can take damage and deliver it just by holding your shield.
The Final skill is obviously "Wrath of the Goddess". Your Aspis now richochets off enemies. It can ricochet up to 4 times. Each time it ricochets it loses 33% of its damage. This skill is useful for applying elements to enemies. If you absorbed cryo, you throw your shield and 4 enemies might be frozen, begging for you to melee them. Even though it loses power after each ricochet it still manages to output serious power.

To recap, you should have:

5 Points in "Ephodos"
5 Points in "Vanguard"
5 Points in "Hold the Line"
1 Point in "Prismatic Aegis"
5 Points in "Return Fire"
1 Point in "Wrath of the Goddess"

You should now only have 3 points leftover.

You now have 3 remaining points to spend. I put my remaining points into "Invictus" for extra Aspis damage, but here is a list of combinations you can make with the remaining points:

3 points into "Prepare for Glory" - Extra gun damage while holding aspis
3 points into "Omega-Senshu" - Extra melee damage to finish off enemies
3 points ino "Tear" - Extra gun damage against bleeding enemies
1 point in "Clear!", 1 point in "Epicenter", 1 point in "Maelstrom" - they all only need 1 point
3 points into "Storm-Weaving" - Increased elemental effect chance and increased fire-rate

I already mentioned some skills, but here is the full list of skills to not put 5 points into.
(i will make it quick)

"United Front" - Shield Regen and Max Shield Capacity hinder the build.
"Stalwart" - If you play solo, it is useless and the health buff is made useless by "Clarity of Purpose"
"You've Got Red On You" - Unless you need health desperately, you won't be making enemies bleed often enough to take advantage of the skill.
"Fury of the Arena" - Melee build. It buffs reload speed and fire rate for each bleeding enemy. MELEE BUILD!!!!

Melee Athena isn't just about the skilltree. A good set of gear used properly with the tree is key, and this is pretty good I think. So here we go!!

Guns

Your primary weapon is the "Excalibastard"



The gun already packs a punch and to sweeten it up it had to have a blade to increase melee damage. Since it always comes in cryo you can freeze an enemy to boost your melee damage even further. Meleeing an enemy with this gun while the enemy is effected by an element will create a nova of that element that sucks enemies into it. The melee itself can freeze enemies too. It is perfect for the build. I think its ... pretty COOL!

Your Secondary weapon is the "Fridgia"



It has a high freeze chance, shoots lots, and is very reliable. It has 127% recoil reduction on it, so the gun never loses the accuracy it has, although it is a very close quarters weapon. It is great for shooting flying enemies thanks to the way the bullets shoot and once they are frozen they are easy to take out with your melee.

Your Healing weapon is "Miss Moxxis Probe"



This gun has terrible damage output. Never use it for sheer damage output. Being a Moxxi weapon, it will heal you based on a percent of damage you did. The weapon used to heal for 65% of damage dealt while holding it! Apparently, we were explpoiting the weapon, and it was reduced to 2% (or something like that). It still heals and is still good to keep, but it doesn't like it used to.

Your Second Wind Machine is "The Nukem"



This rocket launcher has super high damage and is great for second winds. You can use it against frozen enemies if you must, but it is best to save the ammo and the reload time for desperate situations.

Shield

Your shield is the one you all probably guessed, the "Shooting Star"


This amazing thing has one of the highest roid damages in the game, and with a 10 second recharge delay it won't instantly recharge before you can even make use of it. When the shield is empty, your melee will get an extra 15,000 damage added to it! It can have Corrosive, Shock, Cryo or Fire resistance which makes it even more amazing. If you want to be a hipster, you can use the Avalanche shield.

The Class Mod

The Class Mod is the "Vicious Blademaster"


The Class Mod Boosts Melee Damage by 45% and Critical hit damage by 31%. Your statistics may vary, but it should be around those. Both those are great for the "Excalibastard" since it gains boosted critical damage and has a melee damage bonus. It complements the gun perfectly.
The Vicious Blademaster also adds points into great skills in the tree.
My one adds 5 points to "Gun Kata", increasing the 15% gun damage and 50% melee damage to a massive 30% gun damage 100% melee damage!
It adds 4 points into "Mercurial" increasing the power of them to 36% extra movement speed and 31% extra damage resistance.
The class mod also boosts "Clarity of Purpose" by 4 points. Melee damage is increased by 45% and health by 27%.

Grenade Mod

We are using the "Storm Front"


The Storm Front is great for dps and for emptying your shield without killing you. You won't get a damage over time effect from it either. You can use it in other Athena builds and the grenade is very versatile in general. It is good for everything.

Oz Kit

The Oz Kit is an "Acrobat Oz Kit"


Try to get the Oz kit with the Arctic Pre-Fix so it has a cryo butt slam. But we have this so we can have a movement speed buff when we butt slam. You will move 52% faster after butt slamming for a short time, which helps you kill more enemies and just to speed around Elpis faster in general.

How can you get badass gear without knowing where to get it?

The Excalibastard
The Excalibastard can be located in Stantons Liver near the first group of enemies.



You will find the gun sticking out of the ground from the blade. You need a badass rank of at least 2500 to take it out of the ground. Also, you can only get it once ever for each character, so wait until your character is level 50 before getting it. When you get it, it will be the level you take it out of the stone.



Miss Moxxis Probe
Miss Moxxis Probe is a weapon needed to complete the mission "Torgue-o, Torgue-o". Janie Springs will give it to you after you have gotten the Orbatron from her. Janie Springs will be in the building you spawn in at Serenity's Waste or Concordia once you have gotten there and found the jamming signal.



The Fridgia
The Fridgia is a mission reward from Lazlo in the veins of Helios. You must complete "Quarintine: Back On Shcedule" and "Quarintine: Infestation" before you can accept Lazlo's mission, "In Perfect Hibernation". To get the first Quarintine mission go to the bounty board in Handsome Jacks office. To gain the second Quarintine mission, just complete the first mission. It will be at the end of that one. To get the mission "In Perfect Hibernation" you need to finish the second quarintine mission and Tassitor will tell you to talk to the bothered boil.

Once you complete the mission, Lazlo will give you the Fridgia.

The Nukem
The Nukem is a rare drop from Flameknuckle at the start of the game. To get a level 50 Nukem, you need to start ultimate vault hunter mode and kill him. You must kill him, not his power suit. If he doesn't drop the Nukem, restart the story and try again. Flameknuckle is right at the begginning so it isnt a very long farm. If you have the Holodome dlc you can farm flameknuckle from the badass round that you get.

The Shooting Star
The Shooting Star shield is a rare drop from the Noob Power Suit that features in the mission "Red, Then Dead". The mission can be accepted at the Lunar Launching Station bounty board. The Noob Power Suit does not respawn*, so you need to back up your save file or alt+f4 your game otherwise he will not come back.

*Edit: The Noob Power Suit, as well as many other sidequest enemies, has since been patched to respawn after you save and quit.

The Storm Front
The Storm Front can be obtained by grinding 3 grenade mods or finding it from a chest. I got my Storm Front while farming the 2 hyperion chests in The Research and Development area of the game. You can also farm Felicity Rampant for Quasar grenades and grind them together for a chance to get the storm front.
The 2 hyperion chests are here in Research and Development

The X-STLK-23 (custom stalker) is near the chests and he drops the Eridian Vanquisher Class mod for all classes. you can kill him as part of your farm for a legendary.

Vicious Blademaster Class Mod
The Vicious Blademaster Class Mod can be obtained from the Invincible Sentinal, The regular Sentinal, Iwajira and chests. I got my one from Iwajira.

Acrobat Oz Kit
The Acrobat Oz Kit, again can be obtained from the Invincible Sentinal, The regular sentinal, Iwajira and chests. I also got this one from Iwajira. Try to get a Cryo element one. Any element will do, but Cryo is the best.

Congratulations! You have all your gear, and have an awesome skilltree that will help you out on elpis.
And Congratulations to you for reading through my Level 50 Melee Athena Build!

Since I do not have the Holodome DLC (and don't intend on getting it) I won't be doing level 60 guides.

Speaking of guides, this is my Very first guide ever. Tips and feedback will be apreciated in the comments. Is my build complete garbage? is it really good? did i write and layout things well? I would love all the feedback i could get. Also this was a tonne of fun to make and even if everyone hates it, im still glad i made one. If you are considering mading a guide just go ahead. I have had loads of fun making it.

Anyway, have fun cutting stuff up with Athena. Athena is my favourite character in tps and I have another non-melee build for her that I would love to make if this recieves positive feedback.
Thanks for reading, and have a good time :D