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