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