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.
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 on equal terms.
Dealt 99,999 damage with a single attack.
Defeated every worthy opponent.
Responded swiftly to the appearance of enemies.
Fully developed all abilities.
Befriended a most unfriendly monster.
Defeated a powerful enemy with perfect execution.
Turned your back on empty dreams and joined the battle to save mankind.
Went the distance on chocobo-back.
Amassed a fortune in casino coins.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Spent a fortune at shops.
Defeated a powerful enemy with valiant skill.
Obtained five Cinematic Bonus rewards.
Completed an entire fragment category.
Successfully used Feral Link abilities a significant number of times.
Acknowledged the threat facing the world, and decided to fight back.
Performed a multitude of paradigm shifts.
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.
Left behind a normal life, and began a journey through time.
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.
Accepted a new fate in a world where everything has changed.