Here is the full list of all 66 Crystal Story II achievements.
Defeat the "Snowy Chillers" (Hard Mode) in the Battle Arena.
Defeat the "Earth, Wind and Fire" 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.
Complete Chapter V.
Complete all Wanted Quests
Complete the Trickster tree.
Complete the Guardian tree.
Defeat all match defense quests.
Use "Lucky Strike" in battle.
Use "Dragon's Breath" in battle.
Complete the Healer tree.
Complete the Mage tree.
Complete the Thief tree.
Defeat the "Highlands Flyers" in the Battle Arena.
Complete the Slayer tree.
Complete Chapter IV.
Defeat the "Royalty" in the Battle Arena.
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 "Desert Crawlers" in the Battle Arena.
Complete Chapter II.
Defeat "The Dead" in the Battle Arena.
Win 5 Class C Card battles.
Use "Dragon's Roar" in battle.
Win 5 Class D Card battles.
Defeat the "Small Town Gang" in the Battle Arena.
Defeat "The Small 3" in the Battle Arena.
Complete Chapter I.
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.
Successfully hack all of the hackable chests.
Complete the Secret Quest.
Defeat the "Highlands Flyers" (Hard Mode) in the Battle Arena.
Defeat "The Big 3" in the Battle Arena.
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.