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