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