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