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