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.
Completed every fragment category.
Defeated a powerful enemy on equal terms.
Went the distance on chocobo-back.
Performed a multitude of paradigm shifts.
Fully developed all abilities.
Befriended a most unfriendly monster.
Followed the story to its conclusion.
Defeated every worthy opponent.
Obtained the highest possible result in the battle to determine the fate of the world.
Dealt 99,999 damage with a single attack.
Defeated a powerful enemy with perfect execution.
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.
Responded swiftly to the appearance of enemies.
Amassed a fortune in casino coins.
Spent a fortune at shops.
Completed an entire fragment category.
Obtained five Cinematic Bonus rewards.
Defeated a powerful enemy with valiant skill.
Successfully used Feral Link abilities a significant number of times.
Acknowledged the threat facing the world, and decided to fight back.
Fought a significant number of battles without using the "Retry" option.
Visited the place where the saviors of the past dream in crystal.
Performed a significant number of preemptive strikes.
Staggered a significant number of enemies.
Visited the place where clues to the future lie waiting to be discovered.
Defeated a powerful enemy with graceful poise.
Defeated an army's worth of enemies.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.