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