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.
Performed a multitude of paradigm shifts.
Successfully used Feral Link abilities a significant number of times.
Dealt 99,999 damage with a single attack.
Went the distance on chocobo-back.
Responded swiftly to the appearance of enemies.
Defeated a powerful enemy on equal terms.
Befriended a most unfriendly monster.
Fully developed all abilities.
Defeated every worthy opponent.
Defeated a powerful enemy with graceful poise.
Amassed a fortune in casino coins.
Spent a fortune at shops.
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.
Completed an entire fragment category.
Obtained five Cinematic Bonus rewards.
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.
Acknowledged the threat facing the world, and decided to fight back.
Performed a significant number of preemptive strikes.
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.
Fought a significant number of battles without using the "Retry" option.
Staggered a significant number of enemies.
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.