Here is the full list of all 13 HellStar Squadron achievements.
Beat the game on Veteran.
Beat the game on Hard.
Beat the Boss Rush mode.
Beat the game with Citrine.
Beat the game with Azure.
Unlock Niji.
Beat the Game with Niji.
Beat the game with Emerald.
Attain a x100 combo.
Destroy a total of 500 enemy ships.
Clear a stage without getting hit.
Destroy a total of 250 enemy ships.
Attain a x50 combo.