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.
Responded swiftly to the appearance of enemies.
Completed every fragment category.
Obtained five Cinematic Bonus rewards.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Followed the story to its conclusion.
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.
Successfully used Feral Link abilities a significant number of times.
Performed a multitude of paradigm shifts.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Defeated every worthy opponent.
Went the distance on chocobo-back.
Amassed a fortune in casino coins.
Defeated a powerful enemy with valiant skill.
Completed an entire fragment category.
Acknowledged the threat facing the world, and decided to fight back.
Spent a fortune at shops.
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.
Performed a significant number of preemptive strikes.
Staggered a significant number of enemies.
Defeated an army's worth of enemies.
Fought a significant number of battles without using the "Retry" option.
Fully developed all abilities.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.