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