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