Here are the locations of almost all the crystals but some may be miscalculated. Tell me if im wrong...
TIE Construction Yard:
Green: After you leave the third large room (counting the first room you are in), it's on top of the stairs.
Trial of Skill:
Purple: Inside a Jedi statue near the left staircase.
Orange: In the left corner of the room you fight a Junk Behemoth.
Purple: Near the end of the last area before the final fight.
Trial of Insight
Green: In a pile of ruble in the bottom right corner of the temple's main room.
Blue: It's in the temple's main room, on the left side walk way, close to the entrance.
Red: After you fight the first Rancor, it's in a small rock to your left.
Purple: After you fight 2 Rancors, when you're standing at the exit. Turn left, it's in a rock on the wall.
Red: After you fight the first AT-ST, it is inside some fire on the right side of the room.
Orange: In the area you fight the second AT-ST, it is just to the left of the entrance.
Green: After you've fought the Bull Rancor; when you go into the next room, it is in the back right corner (behind some plants).
Imperial Raxus Prime:
Blue: In the AT-ST hangar bay, after you've destroyed it, destroy the 2 control panels near the exit (this will open a door in the empty bay). Go to the empty bay, double-jump to the cross bar, double-jump into the open door, turn around and double-jump to the second floor. It's right behind you when you get to the second floor.
Red: The next room, it's on a ledge just to the left of the entrance.
Blue: After you fight Kleef then go back down the elevator, it's behind this elevator.
Orange: When you are fighting the AT-ST, before you destroy it, it's on the walk way on the right side of the room.