Here is the full list of all 15 No Stick Shooter achievements.
Complete a level having taken no damage
Complete Solar System 1.0
Complete Solar System 2.0
Complete Solar System 3.0
Complete all goals
Complete a level using only the Lightning weapon
Complete a level using only the Beam weapon
Kill 1,000 Asteroids
Kill 500 Evaders
Kill 3,000 Spiltters
Repel 175 projectiles
Repel 20 enemies at once!
Get a combo multiplier of 20 or more
Get awarded 50,000 points for a combo
Score more than 200,000 points on a level