This guide is a translation of this guide. I'm sorry for my English, this is Google translator.

In this guide You will find:

• 32 blue orbs fragments
  
• 8 pink orbs fragments
  
• 12 Secret missions
  
• 1 weapon for Dante

In the screenshots there are markers of different colors. Also, to the right of the sections show the number of things that can be found on the mission.
Red - a secret mission.
Blue - a fragment of a blue Orb.
Purple - a fragment of a purple Orb.
Green is Dante's weapon. In the 18th mission Dante will receive a duplicate of this weapon. You will have 2 rocket launchers, which Dante will be able to use at the same time.
In the main menu you can always return to any secret mission.
Every 4 fragments are crafted into a full blue orb which gives you +1 health bar. To get the maximum amount of health, you need to buy 6 blue orbs from the customization menu, complete 12 secret missions, find 32 hidden fragment of blue Orb.
With each purchased blue orb, the price of the subsequent increases.
Ⅰ – 1500 Red Orbs;
Ⅱ – 3500 Red Orbs;
Ⅲ – 6000 Red Orbs;
Ⅳ – 9000 Red Orbs;
Ⅴ – 18000 Red Orbs;
Ⅵ – 40000 Red Orbs;

For collecting all the blue fragments of orbs. You will receive the maximum health bar for all characters and the achievement:

Physical Perfection

Upgrade your vitality gauge to max.

Every 4 fragments are crafted into a full purple orb which gives you +1 devil trigger bars.
With each purchased purple orb, the price of the subsequent increases.
Ⅰ – 3500 Red Orbs;
Ⅱ – 6000 Red Orbs;
Ⅲ – 9000 Red Orbs;
Ⅳ – 18000 Red Orbs;
Ⅴ – 40000 Red Orbs;

For collecting all the purple fragments of orbs. You will receive the maximum devil trigger bars for all characters and the achievement:

The Devil's Own

Upgrade your Devil Trigger Gauge to max.

All blue fragments of orbs in Devil May Cry 1-3 (with screenshots).
https://steamproxy.net/sharedfiles/filedetails/?id=1329946144
All blue fragments of orbs in Devil May Cry 4 (with screenshots).
https://steamproxy.net/sharedfiles/filedetails/?id=880043431
Translation of this guid into Russian language.
https://steamproxy.net/sharedfiles/filedetails/?id=1676696703
Unlock playable character Vergil.
https://steamproxy.net/sharedfiles/filedetails/?id=1720465708

On the first mission only 1 blue orbs fragment. It is located under the destroyed bridge.

The first fragment is in the room where you will find the second "Nidhogg Hatchling". The room has a flimsy floor. Lure there one enemy and the floor will fail. In room from below and is a fragment of Orb.
The first secret mission is in one of the rooms in the hotel, going through the storyline.
The last fragment is in the ruined city location.

A fragment of blue Orb is on the roof. The second roof, which will jump Nero. On this roof, the camera will focus on the demon spire.
The second secret mission and a fragment of a blue Orb are in the same location. At the top of the stairs is a fragment of a blue Orb. The second secret mission is activated at the bottom.

A fragment of purple and blue Orb can be found by going through the storyline. The fragment are in plain sight, hard to miss. To break the wall with graffiti, summon a Nightmare. The Nightmare will break the wall in the building and you can take the blue fragment. A red arrow mark the location where you can find the second Nidhogg Hatchling. You will need to unlock the path to blue orb fragment and secret missions.
Walking down the street, you will come across a white van. Behind it (right on screenshot) is a secret passage with blue a fragment of an Orb and secret mission #3.

The blue fragment can be found by going through the storyline. To go to the secret mission, summon the Nightmare that will break the shelves.
After the battle with the demons climb the stairs, there will be a secret mission.
A fragment of a purple fragment is on top of the passage through which you came. You can jump to it on the beams from above.

This shard of blue Orb can be found by going through the storyline. Hard to miss. To get it You need to buy Air Hike (double jump) and install the hand "Gerbera", which pushes Nero. Or you need to kill all the enemies before the platform collapses. Then the fragment can be taken without "Gerbera".
The secret mission is in front of the second lava Elevator.
After a secret mission, climb up. Behind the bloody portal hides the enemy. Kill him and you will get a fragment of a blue Orb.

A fragment of a blue Orb and a secret mission are in the courtyard with roots. Come as close as possible to the entrance and summon a Nightmare. The secret mission is on a ledge, right above the shard.
In the tomb is a purple and blue fragments. Summon a Nightmare to destroy the wall to the purple fragment. To get a piece of purple Orb, you need to destroy all the coffins and kill all enemies.

A fragment of a blue Orb is on a small ledge. You can get to it by going through the tunnel.
Immediately after the previous blue fragment go a little further down the corridor. To the right of the white balls you can find a gap in which you can find a purple fragment of orb. But to get this shard, You need to destroy all the demons there.
At the top you will see 2 entrances that will be closed during the battle. After the battle, immediately run to right of the doors. Because they'll close. At the top of the tunnel you will find a secret mission.

After you destroy Blood Clot, there will be a cutscene in which the building fell to one floor. Go back to the passage through which you came. On the second floor you will find a secret mission.
In the place where you destroyed the first Blood Clot, jump down and there destroy all the remaining Blood Clot. After their destruction, you will open a passage to the blue Orb and the passage to the weapons for Dante.
A fragment of a purple fragment can be found by going through the storyline.

The first turn or climb to the right, immediately after you have destroyed the Blood Sac.
Going through the storyline, you jump into a secret passage under the statue. Walking through the catacombs, you will climb the stairs. Opposite this staircase you will find a secret mission. Use Dante's demonic form to get there.

To the right of the closed portal is a fragment of a blue Orb. But you can get it only after free Griffon. First, return the Griffin, and then fly it to the fragment. Or you can make a double jump (bounce off the wall) and make a hit, this is enough to jump.
Going on the storyline, you will come across a fork. First, break the Blood Clot at the bottom of the spiral staircase. And then take a piece of purple Orb. The gap in which the fragment is located, immediately around the corner.
The secret mission is on the spot where you break the Blood Clot by going through the storyline.

Behind the first statue of the goddess is a secret passage. Get to the end of the passage. The secret mission and the blue orb fragment are at the top.
To climb up, use the "gerbera" hand. You need move very quickly, because the walls are slippery and Nero will roll down.
At the top is a secret mission. But to get to the fragment, jump on the slippery canvas on the right. Use the "Gerbera" hand.

Originally posted by anders:

To get up the slippery hills you need to use punch line. throw it out and hold "devil buster"(B on xbox controller) to fly on the rocket, that way you can easily climb to the secret mission. and to get to the blue fragment you can scale the big wall to get directly to it. you need to get on your rocket, jump with it (Devil Buster/B) jump normally twice and then a get on it again by holding B and do all three jumps again. the first three jumps almost get you there so it's not that hard.

After the second statue of the goddess, go down. And you will get into the room, as in the screenshot. Use your hands to jump up and walk on the road until you see a large handful of red orbs. In front of these red orbs is hidden a fragment of a blue ball.

Going through the storyline, you will find yourself in a location with falling projections. To get the blue fragment - get to the other side. To get a purple fragment and a secret mission - jump down.


Going through the storyline, you will find location with white orbs. On one of the ledge is a fragment of a purple orb.


In the same location. But you need to jump to the platform a little higher. On the other side will crystal with red orbs. Behind this crystal is a location where you can activate the last secret mission.










It is impossible to miss by going through the storyline. In demonic form, Dante can jump and use the Trickster more than once.

After the first fight with Shadow, follow her. When you go up, there will be 3 red beetles. Defeat all 3 of them before they escape (digging a hole in the ground), then the blue fragment will appear.