Here is the full list of all 32 Final Fantasy XIII-2 trophies - there are 19 bronze, 6 silver, 6 gold and 1 platinum.
Mastered the timeline and obtained every trophy available.
Witnessed every possible Paradox Ending.
Amassed a fortune in casino coins.
Completed every fragment category.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Defeated a powerful enemy with perfect execution.
Obtained five Cinematic Bonus rewards.
Obtained the highest possible result in the battle to determine the fate of the world.
Fully developed all abilities.
Defeated every worthy opponent.
Responded swiftly to the appearance of enemies.
Dealt 99,999 damage with a single attack.
Successfully used Feral Link abilities a significant number of times.
Defeated a powerful enemy with graceful poise.
Spent a fortune at shops.
Went the distance on chocobo-back.
Followed the story to its conclusion.
Performed a multitude of paradigm shifts.
Turned your back on empty dreams and joined the battle to save mankind.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Completed an entire fragment category.
Defeated a powerful enemy with valiant skill.
Acknowledged the threat facing the world, and decided to fight back.
Visited the place where clues to the future lie waiting to be discovered.
Visited the place where the saviors of the past dream in crystal.
Performed a significant number of preemptive strikes.
Fought a significant number of battles without using the "Retry" option.
Defeated an army's worth of enemies.
Staggered a significant number of enemies.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.