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