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