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.
Responded swiftly to the appearance of enemies.
Went the distance on chocobo-back.
Completed every fragment category.
Befriended a most unfriendly monster.
Fully developed all abilities.
Defeated a powerful enemy with graceful poise.
Followed the story to its conclusion.
Defeated a powerful enemy with perfect execution.
Obtained the highest possible result in the battle to determine the fate of the world.
Turned your back on empty dreams and joined the battle to save mankind.
Amassed a fortune in casino coins.
Defeated a powerful enemy on equal terms.
Prepared to face a test of your determination in the rift where hidden truths slumber.
Defeated every worthy opponent.
Successfully used Feral Link abilities a significant number of times.
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.
Performed a multitude of paradigm shifts.
Acknowledged the threat facing the world, and decided to fight back.
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.
Performed a significant number of preemptive strikes.
Staggered a significant number of enemies.
Defeated an army's worth of enemies.
Fought a significant number of battles without using the "Retry" option.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.