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