Here is the full list of all 20 Paper Nebula achievements.
Beat the first boss
Beat the 2nd Boss
Beat the 3rd Boss
Beat the Final Boss
Lose 50 Drones
Unlock the laser beam
Unlock a wing weapon mount
Unlock hull plating
Unlock an ultimate attack
Kill 100 Opponents
Kill 1000 Opponents
Unlock the Shield
Attempt to skip the credits
Watch the full credits
Die within 10 seconds
Finish a zone with only 1 health remaining
Kill an opponent with your shield
Have one of each mount type equiped
Unlock a tail mounted weapon
Reach the first boss without shooting