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.
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.
Spent a fortune at shops.
Responded swiftly to the appearance of enemies.
Performed a significant number of preemptive strikes.
Visited the place where clues to the future lie waiting to be discovered.
Fought a significant number of battles without using the "Retry" option.
Defeated an army's worth of enemies.
Visited the place where the saviors of the past dream in crystal.
Defeated a powerful enemy with graceful poise.
Staggered a significant number of enemies.
Left behind a normal life, and began a journey through time.
Fully developed all abilities.
Accepted a new fate in a world where everything has changed.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Turned your back on empty dreams and joined the battle to save mankind.
Witnessed every possible Paradox Ending.
Followed the story to its conclusion.
Went the distance on chocobo-back.
Amassed a fortune in casino coins.
Completed every fragment category.
Defeated a powerful enemy with perfect execution.
Performed a multitude of paradigm shifts.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Obtained the highest possible result in the battle to determine the fate of the world.