Here is the full list of all 15 Particle Wars achievements.
completed level 3
completed level 4
completed level 5
completed the hardcore level
completed level 2
completed level 1
Defeated your first boss enemy
Started the game
Got 5000 score on Infinite mode
Got 3000 score on Infinite mode
Got 2000 score on Infinite mode
Got 1000 score on Infinite mode
Got 500 score on Infinite mode
Died for the first time
Picked up your first powerup