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.
Went the distance on chocobo-back.
Witnessed every possible Paradox Ending.
Completed every fragment category.
Amassed a fortune in casino coins.
Dealt 99,999 damage with a single attack.
Befriended a most unfriendly monster.
Responded swiftly to the appearance of enemies.
Fully developed all abilities.
Defeated every worthy opponent.
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.
Defeated a powerful enemy with perfect execution.
Turned your back on empty dreams and joined the battle to save mankind.
Performed a multitude of paradigm shifts.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Spent a fortune at shops.
Completed an entire fragment category.
Successfully used Feral Link abilities a significant number of times.
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.
Staggered a significant number of enemies.
Defeated an army's worth of enemies.
Visited the place where clues to the future lie waiting to be discovered.
Visited the place where the saviors of the past dream in crystal.
Defeated a powerful enemy with graceful poise.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.