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.
Obtained the highest possible result in the battle to determine the fate of the world.
Completed every fragment category.
Defeated a powerful enemy on equal terms.
Fully developed all abilities.
Defeated a powerful enemy with graceful poise.
Defeated every worthy opponent.
Spent a fortune at shops.
Followed the story to its conclusion.
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.
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.
Visited the place where clues to the future lie waiting to be discovered.
Performed a significant number of preemptive strikes.
Staggered a significant number of enemies.
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.
Went the distance on chocobo-back.
Amassed a fortune in casino coins.
Responded swiftly to the appearance of enemies.
Performed a multitude of paradigm shifts.
Dealt 99,999 damage with a single attack.
Befriended a most unfriendly monster.