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.
Defeated a powerful enemy with perfect execution.
Defeated a powerful enemy with graceful poise.
Followed the story to its conclusion.
Turned your back on empty dreams and joined the battle to save mankind.
Performed a multitude of paradigm shifts.
Spent a fortune at shops.
Completed an entire fragment category.
Successfully used Feral Link abilities a significant number of times.
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 clues to the future lie waiting to be discovered.
Visited the place where the saviors of the past dream in crystal.
Staggered a significant number of enemies.
Performed a significant number of preemptive strikes.
Left behind a normal life, and began a journey through time.
Defeated an army's worth of enemies.
Fought a significant number of battles without using the "Retry" option.
Accepted a new fate in a world where everything has changed.
Witnessed every possible Paradox Ending.
Amassed a fortune in casino coins.
Responded swiftly to the appearance of enemies.
Completed every fragment category.
Fully developed all abilities.
Defeated every worthy opponent.
Dealt 99,999 damage with a single attack.
Befriended a most unfriendly monster.
Defeated a powerful enemy on equal terms.
Obtained the highest possible result in the battle to determine the fate of the world.