Hard mode - Successfully complete the game on the Normal difficulty to unlock the Hard difficulty.

Infinity mode - Successfully complete the game on the Hard difficulty to unlock the Infinity difficulty.

Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Surprise! (5 points): Attack the enemy without being detected.
Blitzkrieg (10 points): Keep on surprising the enemy.
Infinitely Unobservant (10 points): Keep on getting surprised by the enemy.
Groundbreaking (20 points): Work on your ground combos.
Aerial Acrobat (20 points): Work on your aerial combos.
Down to Earth (20 points): Work on your down strikes.
Stalwart (30 points): Learn every battle skill.
Sagacious (30 points): Learn every spell.
Artistic (30 points): Learn every tune.
Compulsive (50 points): Obtain every item.
Mister Chef (5 points): Improve your cooking skills.
Claridian Chef (10 points): Keep improving your cooking skills.
Aspiring Chemist (5 points): Improve your alchemy skills.
Claridian Mind (10 points): Keep improving your alchemy skills.
Goldsmith (5 points): Improve your forging skills.
Claridian Hammer (10 points): Keep improving your forging skills.
Bestselling Author (5 points): Improve your writing skills.
Claridian Scribe (10 points): Keep improving your writing skills.
High Enchanter (5 points): Improve your enchanting skills.
Claridian Hand (10 points): Keep improving your enchanting skills.
Social Butterfly (10 points): Take advantage of your party's skills.
Filthy Rich (20 points): Gather as much Fol as you can.
Hero of the Millennium (20 points): Defeat as many enemies as you can.
Time for Glasses? (30 points): Keep on clocking hours.
Barrel of Lulz (15 points): Detonate all the barrels in prison.
On the Run (30 points): Deliver Aya to the village without getting hurt.
Rock, Stock, and Barrel (30 points): Use machines of war to destroy your foes.
Capell to the Rescue (30 points): Rescue the imprisoned.
Guardian (30 points): Deliver the villagers without letting any of them perish.
For the Children (30 points): Rescue the child before he gets hurt.
Reckless Driver (30 points): Use the carts in the mine.
The Tide of Battle (20 points): Watch out for the tsunami.
Imperial Guard (20 points): Hurry to the empress.
Marathon Man (20 points): Hurry to the village under attack.

Additionally, there are sixteen secret achievements, three of which are currently unknown:

Hephaestus's Hammer (30 points): Forged an Azureal blade.
Creme de la Creme (30 points): Cooked a Heaven and Earth Dish.
Mad Scientist (30 points): Alchemized a Holy Grail.
Summa Cum Laude (30 points): Wrote "Will of the Universe".
Secret achievement (30 points): Unknown.
Secret achievement (30 points): Unknown.
Azure Avenger (10 points): Destroyed the Azure Chain.
Crimson Crusader (10 points): Destroyed the Crimson Chain.
Orange Officer (10 points): Destroyed the Orange Chain.
Cerulean Savior (10 points): Destroyed the Cerulean Chain.
Amber Ace (10 points): Destroyed the Amber Chain.
Ashen Assailant (10 points): Destroyed the Ashen Chain.
Vengeance at Last (30 points): Defeated the Dreadknight.
Decide (45 points): Defeated Veros.
Big Daddy's Back (49 points): Sigmund joined your party in the Seraphic Gate.
Secret achievement (1 points): Unknown.