What are the Fragment Skills?

Question

I have many of the Fragment Skills in FFXIII-2 but I was wondering what all of them are? Specifically: what skill they grant you and how to attain them in the game.

Answer 1

From http://www.gamefaqs.com/ps3/619315-final-fantasy-xiii-2/faqs/63553

1. Mog's Manifestation (available from start of Episode 4) - Enables gaining special rewards when you throw Mog (ie. guaranteed at least 1 gil, if nothing else). Also needed for special one-off crystals, like Silver Chocobo.
2. Mobile Mog (collect all fragments in Oerba timelines, paradox ending included) - Mog returns much quicker when you throw him.
3. Bargain Hunter (available from start of Episode 6) - Lowers prices (including in the casino, for prizes) by 25%.
4. Haggler (available from start of Episode 4) - Increases amount gained from selling items. I believe this is 25%, will confirm later.
5. Chocobo Music (collect all fragments in the Monster Bits and Bounty Hunter categories including those for the Archylte Steppe bosses) - Lets you change what music plays when you ride a chocobo. Limited to preset chocobo riding music.
6. Anti-Grav Jump (available from start of Episode 6) - Allows you to float for a short period when holding down jump.
7. Field Killer (collect all the fragments in the Academia Reward and Great Mog Wisdom categories) - If the monster is weak enough, autokill when you attack for pre-emptive. Note that this does not award CP or gil. I don't know how it calculates relative strength levels.
8. Monster Collector (collect all fragments from Vile Peaks timelines) - Flat +20% chance to get monster crystals.
9. Encounter Master (collect all fragments from Yaschas Massif timelines) - Raise or lower the encounter rate.
10. Battlemania (obtain all fragments for completing 100% of all maps) - Increased chance of rare encounters (Distortions, especially).
11. Rolling in CP (collect all fragments from Yaschas Massif timelines, and all fragments from Bresha Ruins timelines) - Double CP awarded.
12. Eyes of the Goddess (collect all fragments from AF003 New Bodhum, AF005 Bresha Ruins, AF010 Yaschas Massif, AF01X Yaschas Massif, AF200 Oerba and AF300 Sunleth Waterscape) - Lets you move the camera around during cutscenes.
13. Clock Master (obtain all 160 fragments) - Speed up/slow down game speed. Note that this is basically global; you'll run around faster or slower, too, not just battles.
14. Paradox Scope (beat the game) - Enable certain paradox fights, along with their endings.

Just remember, you have to go back to Serendipity and talk to the lady in the left-most house. The one where Mog is.