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