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