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