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