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