Additional reward: 2500 CP
You’ll obtain this fragment automatically as you progress the game (kill atlas by using the mysterious crystal).
Additional Reward: 200 CP
You’ll obtain this automatically as your progress the game (solving temporal rift puzzle on the crystal to weaken Atlas).
Additional reward: 600 CP
Talk to Soldier who is standing south of point (3), he’ll tell you a story about Cie’th. You can find Cie’th on the same spot where you can find Star Pendant. It’s not hard, just a little bit stronger than ordinary enemies in this area.
Additional Reward: 100 CP
Talk to the soldier who is walking between Reunion Gate and Rune Bracelet. He’ll ask you to find 2 capsules. You can find one easily by using moggle hun to reveal the treasure (See Bresha Ruins Map for the exact location).The second capsule location is a little bit tricky. It’s on the north of 8 Mana droplets treasure chest BUT it’s on the lower floor. See the screenshot below for more detailed info (Click it to enlarge).
Additional Reward: 500 CP
It’s needed to complete the storyline. The fragment is located on the “unexplored area” that located northeast of point (1). You need a chocobo to access this area, so grab one and then jump to the area where the fragment is located (from the northwest). Use moogle hunt to find it and don’t forget to grab 8 power droplets nearby if you haven’t got it before.