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.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Performed a multitude of paradigm shifts.
Fully developed all abilities.
Obtained the highest possible result in the battle to determine the fate of the world.
Amassed a fortune in casino coins.
Went the distance on chocobo-back.
Defeated a powerful enemy with perfect execution.
Completed an entire fragment category.
Defeated a powerful enemy with graceful poise.
Spent a fortune at shops.
Responded swiftly to the appearance of enemies.
Followed the story to its conclusion.
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.
Successfully used Feral Link abilities a significant number of times.
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.
Fought a significant number of battles without using the "Retry" option.
Defeated an army's worth of enemies.
Staggered a significant number of enemies.
Left behind a normal life, and began a journey through time.
Accepted a new fate in a world where everything has changed.