Here is the full list of all 66 Crystal Story II achievements.
Use "Magic Bullet" in battle.
Use "Dragon's Rage" in battle.
Win 5 Class A Card battles.
Win 5 Class B Card battles.
Win 5 Class C Card battles.
Win 5 Class D Card battles.
Defeat the boss of Giant Land.
Complete the bestiary.
Defeat the boss of Lao Prison.
Complete the Secret Quest.
Defeat the boss of Sunken Ruins.
Defeat the "Desert Crawlers" in the Battle Arena.
Defeat "The Big 3" in the Battle Arena.
Win all Mercenary Defense events.
Complete Chapter VI.
Defeat all match defense quests.
Defeat Seraph.
Defeat Foxer.
Complete all Wanted X Quests
Complete all Wanted Quests
Defeat Mechaslime.
Defeat the boss of Doom Lair.
Defeat Calloc.
Defeat the "Snowy Chillers" (Hard Mode) in the Battle Arena.
Defeat the "Highlands Flyers" (Hard Mode) in the Battle Arena.
Defeat the "Swamp Stalkers" (Hard Mode) in the Battle Arena.
Defeat the "Desert Crawlers" (Hard Mode) in the Battle Arena.
Defeat the "Small Town Gang" (Hard Mode) in the Battle Arena.
Defeat the "Snowy Chillers" in the Battle Arena.
Defeat the "Highlands Flyers" in the Battle Arena.
Defeat the "Swamp Stalkers" in the Battle Arena.
Defeat Chimera Prime.
Complete Chapter V.
Use "Hurricane" in battle.
Use "Dragon's Breath" in battle.
Successfully hack all of the hackable chests.
Defeat the "Earth, Wind and Fire" in the Battle Arena.
Defeat the "Royalty" in the Battle Arena.
Use "Snipe" in battle.
Use "Rend" in battle.
Complete the Healer tree.
Complete the Trickster tree.
Complete the Mage tree.
Complete the Guardian tree.
Complete the Slayer tree.
Complete the Thief tree.
Complete Chapter IV.
Defeat "The Dead" in the Battle Arena.
Defeat the "Small Town Gang" in the Battle Arena.
Complete Chapter III.
Use "Cursed Dagger" in battle.
Complete Chapter II.
Use "Dragon's Roar" in battle.
Complete Chapter I.
Defeat "The Small 3" in the Battle Arena.
Win your first battle.
Use "Lucky Strike" in battle.
Use "Cyclone Dance" in battle.
Use "Trigger Happy" in battle.
Use "Death's Gate" in battle.
Catch all the rare fishes.
Get a Gold time on Track 3 of Snowboard Extreme!
Win 5 Class S Card battles.
Win 5 Class GM Card battles.
Defeat the Card Master in a card battle.
Obtain the Number One Card.