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.
Went the distance on chocobo-back.
Completed every fragment category.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Amassed a fortune in casino coins.
Dealt 99,999 damage with a single attack.
Fully developed all abilities.
Defeated every worthy opponent.
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.
Successfully used Feral Link abilities a significant number of times.
Defeated a powerful enemy with valiant skill.
Obtained five Cinematic Bonus rewards.
Completed an entire fragment category.
Performed a multitude of paradigm shifts.
Acknowledged the threat facing the world, and decided to fight back.
Defeated a powerful enemy with graceful poise.
Responded swiftly to the appearance 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.
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.
Staggered a significant number of enemies.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.