Okay, all of us who play the game have one or two Fragments who escape our notice. In this walk-through made by The Phantarch which is the original person who thought the idea of providing walk-through about the Blue Orb Fragments as you can view here we tried to make sure we show you where the Fragments are located. +rep to Phantarch for this
First of all:
What is a Blue Orb?
Blue Orb: This orb increases your character's maximum vitality. You can buy Blue Orbs at the Time God's Statue by using Red Orbs. The currency used in Devil May Cry which is acquired by killing enemies, taking it as a bonus at the end of each mission or just found it throughout the game. There are times where you can find a Blue Orb just lying somewhere while playing a mission but most of the times you'll end up finding a Blue Orb Fragment. As a side note, if you are low on health and you find a Blue Orb you health will fill completely along with maximizing itself.
What is a Blue Orb Fragment?
Blue Orb Fragment: It is a Blue Orb which is shattered in 4 pieces. When you find 4 of them, they automatically combine into a whole Blue Orb and increase your character's vitality.
In this thread we tried to show you all the locations of Blue Orb Fragments/Blue Orbs that you cannot buy. All credit to the Phantarch and to me for posting this and finding 4 or 5 Fragments that Phantarch forgot
.
As a side note you can view in videos where the Blue Orb Fragments are in this thread.
Mission 01.
1) After the cut-scenes when you finally get to play you pass under something like a bridge. Go up on it and walk to its end which is somehow enclosed. You should get a fragment there.
2) In the first room after the "Mission Start" shows up. This orb is on a floor path near the left stairway, against the left wall. You use the double-jump against the wall to reach it. Then get the Blue Orb fragment inside.
3) In the room you opened using Red Orbs. The orb is in the suits of armor. Strike them to get it along with the Red Orbs.
4) After running up the stairs and entering the wooden door. In the right area of the room with the gate mechanism (has a gargoyle of some sort that has "three indentations", you can jump to the upper water to get a Blue Orb piece beside it.
5) In the room you unlocked with the key. This orb is on the left wing of the airplane in the room with the lift.
Mission 02.
6) After you start the mission go left and enter the door. Break table in room left of divinity statue for it.
Mission 03.
7) After you defeat the Phandom go back to where the stair was and fell in the ocean.This is the 1st Secret Mission. Try to kill this guy with one shot and you'll get a Blue Orb Fragment. Shotgun is your best friend here.
8) After the Secret Mission go to the place with the red orbs at the end of the broken bridge. A fragment should now be there.
9) Before you enter in the place you beat Phandom try to climb a bit over the door, to the highest position, then use stinger to get it.
Mission 04.
10) After you deal with Phandom again go back to the door in which Alastor was. Inside is another Secret Mission. Ebony & Ivory do the job nicely there.
11) Now go back to the place you got the 6th Fragment. There is another Secret Mission there. And Alastor's fast running with DT helps a lot.
12) Now I think that to do this Secret Mission you must have beaten the Shadow/Death Scythe 1st. Anyway go back to the airplane room and as in the 1st mission hit that thingy to go down with the elevator. For me this is the most difficult Secret Mission. Try to evade as much as you can.
Mission 05.
13) After you finish the Shadow(s) and climb up all the way you climbed while fighting Nelo Angelo you can see a Fragment if you double jump in the end of the "road" just near the "hole" in which you must fall in and enter the door. Don't fall there. Just look as left it can be seen and there is a place in which you can go with double jump. From this place again with double jump(I am referring to Air Hike
) you can get the Fragment.
Mission 06.
14) Just after you begin the mission go to your character's right and try to enter some sort of hole. You will fail but the Fragment will come.
Mission 07.
15) After you beat the Sins/Frosts enter the room from which the flies came. There is another Secret Mission. If you time it correctly both monsters will shoot rocks at one another killing each other.
Mission 08.
16) After you beat Phandom and the door opens instead o just jumping down from the open door use Stinger. Your character will land on the Fragment. Alternative, you can fall and see that there's hole in the floor between the statues of two horses. Above it, you can see a glowing Blue Orb Fragment. Just try to jump up to the either horse's head, not the back. Try to reach the head, then kick jump to the top to get the Blue Orb Fragment.
17) Remember in the 1st mission that you jumped in the left hole with water and there was a fragment. Now there's another one.
18) Now in the opened steel door you can access these water places. Jump on the right one and gain another fragment.
Mission 09.
19) In the area where you encounter the blades, you run to the right side from the entrance, as far as you can,until you find a tombstone. This tombstone is movable. Hit it to move it. It will reveal a Blue Orb Fragment.
Mission 10.
It has no Fragments scattered or any Secret Missions.
Mission 11.
20) Defeat the Blades that are inside that hole you see at the beginning of the mission and a fragment will fall.
21) After you beat the Death guy, go back from the door which is behind you at the beginning of the mission. It's a Secret Mission. Kick Jump and Air Hike work well here.
22) In the first room of the mission use that platform that appears after you killed the Death guy and jump in a place which looks secluded with a roof. In there you should go as down as you can and see the fragment.
Mission 12.
23) South of the ship. Get to highest point and use stinger to get a far-away Blue Orb Fragment.
Mission 13.
24) After you kill the 1st Blades do not enter the room in which you should in order to continue going out of the ship. Instead if you look well there is another door which leads to more Blades but also another Fragment.
Mission 14.
25) Go back in the ship, in the place you got the Staff of Hermes and speak to the corpse of the captain. It is a Secret Mission. The better you are at shooting with Needle-gun the easier the mission will be.
26) After you walk on solid earth again go as right of the ship as you can and then jump again into the water. Another Fragment awaits.
26) In the area with the waterfall and the divinity statue; a Blue Orb piece, Red Orbs and Yellow Orbs are all here. They are on one of the high ledges around the area. Either Air Raid or Air Hike required to get them. Jump from the low ledges to high ones until you find them.There's an easy way to get the Blue Orb Fragment. Just stand near the elevator you have got down, then run and Air Hike to the opposite ledge which has the Blue Orb Fragment on it.
27) In the next area there is another Fragment near the wooden bridge. Just jump towards it.
Mission 15.
28) Go back to the place where you activated that mechanism with needles in the previous mission. In the corridor which does not have needles speak to some sort of symbol on the wall. The 2nd most difficult Secret Mission.
29) In the room with the Blue Shield Emblem smash the half broken wall along with everything else inside. You should see it.
30) In the room with the Red Shield Emblem go where the Pair of Lances are and jump down to face the Shadows, you don't need to beat them. If you just fall there the Blue Orb Fragment will appear near the Lances.
31) In the place you fight Griffon before you fight him, climb as up as you can and when you'll come at the center of that "bridge" a Fragment should appear.

First of all:
What is a Blue Orb?

Blue Orb: This orb increases your character's maximum vitality. You can buy Blue Orbs at the Time God's Statue by using Red Orbs. The currency used in Devil May Cry which is acquired by killing enemies, taking it as a bonus at the end of each mission or just found it throughout the game. There are times where you can find a Blue Orb just lying somewhere while playing a mission but most of the times you'll end up finding a Blue Orb Fragment. As a side note, if you are low on health and you find a Blue Orb you health will fill completely along with maximizing itself.
What is a Blue Orb Fragment?

Blue Orb Fragment: It is a Blue Orb which is shattered in 4 pieces. When you find 4 of them, they automatically combine into a whole Blue Orb and increase your character's vitality.
In this thread we tried to show you all the locations of Blue Orb Fragments/Blue Orbs that you cannot buy. All credit to the Phantarch and to me for posting this and finding 4 or 5 Fragments that Phantarch forgot

As a side note you can view in videos where the Blue Orb Fragments are in this thread.

Mission 01.
1) After the cut-scenes when you finally get to play you pass under something like a bridge. Go up on it and walk to its end which is somehow enclosed. You should get a fragment there.
2) In the first room after the "Mission Start" shows up. This orb is on a floor path near the left stairway, against the left wall. You use the double-jump against the wall to reach it. Then get the Blue Orb fragment inside.
3) In the room you opened using Red Orbs. The orb is in the suits of armor. Strike them to get it along with the Red Orbs.
4) After running up the stairs and entering the wooden door. In the right area of the room with the gate mechanism (has a gargoyle of some sort that has "three indentations", you can jump to the upper water to get a Blue Orb piece beside it.
5) In the room you unlocked with the key. This orb is on the left wing of the airplane in the room with the lift.
Mission 02.
6) After you start the mission go left and enter the door. Break table in room left of divinity statue for it.
Mission 03.
7) After you defeat the Phandom go back to where the stair was and fell in the ocean.This is the 1st Secret Mission. Try to kill this guy with one shot and you'll get a Blue Orb Fragment. Shotgun is your best friend here.
8) After the Secret Mission go to the place with the red orbs at the end of the broken bridge. A fragment should now be there.
9) Before you enter in the place you beat Phandom try to climb a bit over the door, to the highest position, then use stinger to get it.
Mission 04.
10) After you deal with Phandom again go back to the door in which Alastor was. Inside is another Secret Mission. Ebony & Ivory do the job nicely there.
11) Now go back to the place you got the 6th Fragment. There is another Secret Mission there. And Alastor's fast running with DT helps a lot.
12) Now I think that to do this Secret Mission you must have beaten the Shadow/Death Scythe 1st. Anyway go back to the airplane room and as in the 1st mission hit that thingy to go down with the elevator. For me this is the most difficult Secret Mission. Try to evade as much as you can.
Mission 05.
13) After you finish the Shadow(s) and climb up all the way you climbed while fighting Nelo Angelo you can see a Fragment if you double jump in the end of the "road" just near the "hole" in which you must fall in and enter the door. Don't fall there. Just look as left it can be seen and there is a place in which you can go with double jump. From this place again with double jump(I am referring to Air Hike

Mission 06.
14) Just after you begin the mission go to your character's right and try to enter some sort of hole. You will fail but the Fragment will come.
Mission 07.
15) After you beat the Sins/Frosts enter the room from which the flies came. There is another Secret Mission. If you time it correctly both monsters will shoot rocks at one another killing each other.
Mission 08.
16) After you beat Phandom and the door opens instead o just jumping down from the open door use Stinger. Your character will land on the Fragment. Alternative, you can fall and see that there's hole in the floor between the statues of two horses. Above it, you can see a glowing Blue Orb Fragment. Just try to jump up to the either horse's head, not the back. Try to reach the head, then kick jump to the top to get the Blue Orb Fragment.
17) Remember in the 1st mission that you jumped in the left hole with water and there was a fragment. Now there's another one.
18) Now in the opened steel door you can access these water places. Jump on the right one and gain another fragment.
Mission 09.
19) In the area where you encounter the blades, you run to the right side from the entrance, as far as you can,until you find a tombstone. This tombstone is movable. Hit it to move it. It will reveal a Blue Orb Fragment.
Mission 10.
It has no Fragments scattered or any Secret Missions.
Mission 11.
20) Defeat the Blades that are inside that hole you see at the beginning of the mission and a fragment will fall.
21) After you beat the Death guy, go back from the door which is behind you at the beginning of the mission. It's a Secret Mission. Kick Jump and Air Hike work well here.
22) In the first room of the mission use that platform that appears after you killed the Death guy and jump in a place which looks secluded with a roof. In there you should go as down as you can and see the fragment.
Mission 12.
23) South of the ship. Get to highest point and use stinger to get a far-away Blue Orb Fragment.
Mission 13.
24) After you kill the 1st Blades do not enter the room in which you should in order to continue going out of the ship. Instead if you look well there is another door which leads to more Blades but also another Fragment.
Mission 14.
25) Go back in the ship, in the place you got the Staff of Hermes and speak to the corpse of the captain. It is a Secret Mission. The better you are at shooting with Needle-gun the easier the mission will be.
26) After you walk on solid earth again go as right of the ship as you can and then jump again into the water. Another Fragment awaits.
26) In the area with the waterfall and the divinity statue; a Blue Orb piece, Red Orbs and Yellow Orbs are all here. They are on one of the high ledges around the area. Either Air Raid or Air Hike required to get them. Jump from the low ledges to high ones until you find them.There's an easy way to get the Blue Orb Fragment. Just stand near the elevator you have got down, then run and Air Hike to the opposite ledge which has the Blue Orb Fragment on it.
27) In the next area there is another Fragment near the wooden bridge. Just jump towards it.
Mission 15.
28) Go back to the place where you activated that mechanism with needles in the previous mission. In the corridor which does not have needles speak to some sort of symbol on the wall. The 2nd most difficult Secret Mission.
29) In the room with the Blue Shield Emblem smash the half broken wall along with everything else inside. You should see it.
30) In the room with the Red Shield Emblem go where the Pair of Lances are and jump down to face the Shadows, you don't need to beat them. If you just fall there the Blue Orb Fragment will appear near the Lances.
31) In the place you fight Griffon before you fight him, climb as up as you can and when you'll come at the center of that "bridge" a Fragment should appear.