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