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.
Went the distance on chocobo-back.
Witnessed every possible Paradox Ending.
Completed every fragment category.
Successfully used Feral Link abilities a significant number of times.
Defeated a powerful enemy on equal terms.
Defeated a powerful enemy with perfect execution.
Befriended a most unfriendly monster.
Fully developed all abilities.
Defeated every worthy opponent.
Performed a multitude of paradigm shifts.
Dealt 99,999 damage with a single attack.
Amassed a fortune in casino coins.
Responded swiftly to the appearance of enemies.
Obtained five Cinematic Bonus rewards.
Followed the story to its conclusion.
Obtained the highest possible result in the battle to determine the fate of the world.
Spent a fortune at shops.
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.
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.
Defeated a powerful enemy with graceful poise.
Staggered a significant number of enemies.
Fought a significant number of battles without using the "Retry" option.
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.