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.
Befriended a most unfriendly monster.
Went the distance on chocobo-back.
Defeated a powerful enemy on equal terms.
Defeated every worthy opponent.
Fully developed all abilities.
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.
Spent a fortune at shops.
Successfully used Feral Link abilities a significant number of times.
Defeated a powerful enemy with perfect execution.
Turned your back on empty dreams and joined the battle to save mankind.
Dealt 99,999 damage with a single attack.
Amassed a fortune in casino coins.
Performed a multitude of paradigm shifts.
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.
Completed an entire fragment category.
Acknowledged the threat facing the world, and decided to fight back.
Visited the place where the saviors of the past dream in crystal.
Performed a significant number of preemptive strikes.
Visited the place where clues to the future lie waiting to be discovered.
Defeated a powerful enemy with graceful poise.
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.