Here is the full list of all 66 Crystal Story II achievements.
Defeat "The Big 3" in the Battle Arena.
Defeat the "Snowy Chillers" in the Battle Arena.
Defeat the "Highlands Flyers" (Hard Mode) in the Battle Arena.
Defeat the "Swamp Stalkers" (Hard Mode) in the Battle Arena.
Win 5 Class S Card battles.
Successfully hack all of the hackable chests.
Defeat the "Desert Crawlers" (Hard Mode) in the Battle Arena.
Defeat the "Small Town Gang" (Hard Mode) in the Battle Arena.
Complete Chapter V.
Use "Lucky Strike" in battle.
Complete all Wanted Quests
Use "Dragon's Breath" in battle.
Defeat the "Earth, Wind and Fire" in the Battle Arena.
Complete the Healer tree.
Complete the Thief tree.
Complete the Guardian tree.
Defeat all match defense quests.
Win 5 Class A Card battles.
Complete the Mage tree.
Complete the Trickster tree.
Complete the Slayer tree.
Use "Cursed Dagger" in battle.
Defeat the "Highlands Flyers" in the Battle Arena.
Complete Chapter IV.
Use "Snipe" in battle.
Use "Rend" in battle.
Defeat the "Royalty" in the Battle Arena.
Defeat the "Swamp Stalkers" in the Battle Arena.
Win 5 Class B Card battles.
Complete Chapter III.
Use "Dragon's Roar" in battle.
Defeat the "Desert Crawlers" in the Battle Arena.
Complete Chapter II.
Defeat "The Dead" in the Battle Arena.
Win 5 Class C Card battles.
Win 5 Class D Card battles.
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 the boss of Doom Lair.
Defeat Calloc.
Defeat Mechaslime.
Defeat Chimera Prime.
Defeat Foxer.
Defeat Seraph.
Use "Dragon's Rage" in battle.
Use "Cyclone Dance" in battle.
Use "Magic Bullet" in battle.
Use "Trigger Happy" in battle.
Use "Hurricane" 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.
Defeat the "Snowy Chillers" (Hard Mode) in the Battle Arena.
Win 5 Class GM Card battles.
Defeat the Card Master in a card battle.
Obtain the Number One Card.