Here is the full list of all 33 Cosmic Star Heroine achievements.
Win first battle in game on hardest difficulty level
Complete the game
Defeat a special bounty
Find the ultimate ingredient
Defeat the Prime Evil
Reclaim your high score
Gain at least 20 recruits for your ship
A party member betrays you
Defeat a cosmic entity
Defeat a true hero
Gain Chahn's ultimate ability
Defeat the ultimate zombie
Deal over 9999 damage in a single hit
Scare rats away in Gehenna
Gain your final party member
Prove your innocence
Defeat the Crystal Wraith
Defeat the Nightmare
Escape confinement
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
Charm an enemy
Defeat Spectral Dragon
Defeat the lab guardian
Win a VR Battle
Share a soda
Complete SkyBreaker Tower scenario