Here is the full list of all 33 Cosmic Star Heroine achievements.
Complete the game
Reclaim your high score
Defeat the Prime Evil
A party member betrays you
Defeat a special bounty
Gain at least 20 recruits for your ship
Gain Chahn's ultimate ability
Find the ultimate ingredient
Gain your final party member
Defeat a true hero
Prove your innocence
Defeat a cosmic entity
Win a VR Battle
Defeat the ultimate zombie
Defeat the Crystal Wraith
Defeat the Nightmare
Escape confinement
Deal over 9999 damage in a single hit
Use Clarke's Self-Destruct ability
Use a Heroine program
Chat with your party members
Commandeer your own spaceship
Defeat the Blobmith
Win every round of Rock Paper Scissors
Reach Lauren's apartment
Charm an enemy
Scare rats away in Gehenna
Reach 300 Style
Defeat Spectral Dragon
Defeat the lab guardian
Share a soda
Complete SkyBreaker Tower scenario
Win first battle in game on hardest difficulty level