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.
Befriended a most unfriendly monster.
Amassed a fortune in casino coins.
Went the distance on chocobo-back.
Responded swiftly to the appearance of enemies.
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.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Fully developed all abilities.
Performed a multitude of paradigm shifts.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Spent a fortune at shops.
Completed an entire fragment category.
Defeated a powerful enemy with valiant skill.
Obtained five Cinematic Bonus rewards.
Successfully used Feral Link abilities a significant number of times.
Acknowledged the threat facing the world, and decided to fight back.
Visited the place where the saviors of the past dream in crystal.
Defeated a powerful enemy with graceful poise.
Visited the place where clues to the future lie waiting to be discovered.
Performed a significant number of preemptive strikes.
Left behind a normal life, and began a journey through time.
Fought a significant number of battles without using the "Retry" option.
Defeated an army's worth of enemies.
Staggered a significant number of enemies.
Accepted a new fate in a world where everything has changed.