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.
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.
Completed an entire fragment category.
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.
Acknowledged the threat facing the world, and decided to fight back.
Spent a fortune at shops.
Performed a significant number of preemptive strikes.
Defeated every worthy opponent.
Fought a significant number of battles without using the "Retry" option.
Dealt 99,999 damage with a single attack.
Defeated an army's worth of enemies.
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.
Staggered a significant number of enemies.
Defeated a powerful enemy with graceful poise.
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.
Successfully used Feral Link abilities a significant number of times.
Performed a multitude of paradigm shifts.
Fully developed all abilities.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.