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.
Amassed a fortune in casino coins.
Witnessed every possible Paradox Ending.
Completed every fragment category.
Went the distance on chocobo-back.
Befriended a most unfriendly monster.
Performed a multitude of paradigm shifts.
Defeated a powerful enemy on equal terms.
Fully developed all abilities.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Responded swiftly to the appearance of enemies.
Successfully used Feral Link abilities a significant number of times.
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.
Spent a fortune at shops.
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.
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.
Staggered a significant number of enemies.
Performed a significant number of preemptive strikes.
Fought a significant number of battles without using the "Retry" option.
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.