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