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