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.
Performed a multitude of paradigm shifts.
Went the distance on chocobo-back.
Fully developed all abilities.
Successfully used Feral Link abilities a significant number of times.
Witnessed every possible Paradox Ending.
Befriended a most unfriendly monster.
Completed every fragment category.
Defeated a powerful enemy on equal terms.
Dealt 99,999 damage with a single attack.
Defeated every worthy opponent.
Defeated a powerful enemy with graceful poise.
Responded swiftly to the appearance of enemies.
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.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Completed an entire fragment category.
Obtained five Cinematic Bonus rewards.
Defeated a powerful enemy with valiant skill.
Acknowledged the threat facing the world, and decided to fight back.
Amassed a fortune in casino coins.
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.
Performed a significant number of preemptive strikes.
Fought a significant number of battles without using the "Retry" option.
Staggered a significant number of enemies.
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.