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.
Went the distance on chocobo-back.
Responded swiftly to the appearance of enemies.
Defeated a powerful enemy with graceful poise.
Fully developed all abilities.
Followed the story to its conclusion.
Obtained the highest possible result in the battle to determine the fate of the world.
Performed a multitude of paradigm shifts.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Successfully used Feral Link abilities a significant number of times.
Amassed a fortune in casino coins.
Spent a fortune at shops.
Completed an entire fragment category.
Defeated a powerful enemy with perfect execution.
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.
Obtained five Cinematic Bonus rewards.
Acknowledged the threat facing the world, and decided to fight back.
Visited the place where the saviors of the past dream in crystal.
Performed a significant number of preemptive strikes.
Visited the place where clues to the future lie waiting to be discovered.
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.