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