Here is the full list of all 15 Particle Wars achievements.
completed the hardcore level
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
completed level 5
completed level 4
Defeated your first boss enemy
completed level 3
completed level 2
completed level 1
Picked up your first powerup