Here is the full list of all 31 Final Fantasy XIII-2 achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Witnessed every possible Paradox Ending.
Went the distance on chocobo-back.
Completed every fragment category.
Defeated a powerful enemy on equal terms.
Befriended a most unfriendly monster.
Dealt 99,999 damage with a single attack.
Defeated every worthy opponent.
Performed a multitude of paradigm shifts.
Fully developed all abilities.
Followed the story to its conclusion.
Obtained the highest possible result in the battle to determine the fate of the world.
Defeated a powerful enemy with perfect execution.
Turned your back on empty dreams and joined the battle to save mankind.
Responded swiftly to the appearance of enemies.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Amassed a fortune in casino coins.
Spent a fortune at shops.
Defeated a powerful enemy with valiant skill.
Obtained five Cinematic Bonus rewards.
Completed an entire fragment category.
Acknowledged the threat facing the world, and decided to fight back.
Successfully used Feral Link abilities a significant number of times.
Visited the place where the saviors of the past dream in crystal.
Visited the place where clues to the future lie waiting to be discovered.
Defeated a powerful enemy with graceful poise.
Staggered a significant number of enemies.
Performed a significant number of preemptive strikes.
Defeated an army's worth of enemies.
Fought a significant number of battles without using the "Retry" option.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.