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