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