Mission Appearance: Mission 3

Location: You can't miss this one. It's on the ledge of a building on the right side of 13th Slum Avenue.

Mission Appearance: Mission 4

Location: This one is high above the green door in Incandescent Space. Jump on the handrail to the right, then jump onto the pipe in front. From there, kick jump the wall and you should be able to get it.

Mission Appearance: Mission 7

Location: This one's on a ledge in the Pitch-black Void. Kick/Double jump onto the middle ledge, then from there jump onto the one with the blue orb fragment.

Mission Appearance: Mission 8

Location: From where you begin the mission, jump onto the higher ledge to the right. Follow it down to the other end where you'll find another tusk seal. Go behind the seal and kick jump the wall to the left. Try landing on the long, pointy part of the ship's deck. It may take a few tries if unlucky. Once on it, carefully walk forward and you should now clearly see the deck as in the picture on the left.

Mission Appearance: Mission 9

Location: This one is very hidden in the Subterranean Garden (where you face your first light puzzle). Stand facing the wall to the left of the Divinity Statue you find there. Do a Wall Hike upwards, and when Dante eventually flips around, perform Air Hike and at the peak of your jump, perform Sky Star. See below:
Video demonstration - Dante

For Vergil, stand facing the wall to the left of the Divinity Statue, then kick jump the wall so that Vergil flips backwards after the jump. When he flips, he faces the screen so you'll have to turn him back towards the wall by performing 1 hit of Aerial Rave in the direction of the wall. After that, perform Trick Up and you should land on the hidden alcove. See below:
Video demonstration - Vergil

Mission Appearance: Mission 11

Location: Once out of the gear room with the Enigmas, jump onto the iron pipes you see above the door to get a view of the blue orb fragment. You know the rest.

Mission Appearance: Mission 14

Location: This one is given to you after you defeat all the Damned Pawns, Knights, Bishops and Rooks.

Mission Appearance: Mission 15

Location: After getting the 3rd Orihalcon, turn on the wheel on the wall in the destroyed Subterranean Lake once. Enter the door to the left of the wheel to find yourself in the path going towards the battle arena where you fought Geryon. Hop off the bridge down to the area and circle around until you find the blue orb fragment lying around.

Mission Appearance: Mission 17

Location: In the moving cubes room, enter the door on the platform you first get onto, only to find yourself facing several Enigmas and 3 Hell Vanguards. Defeat them all, then exit through the other door (red). Follow the path and you'll find a blue orb fragment where the picture on the left shows.

Mission Appearance: Mission 18

Location: Defeat ALL 9 bosses in this mission.