Here is the full list of all 15 StarDrone trophies - there are 13 bronze, 1 silver and 1 gold.
Wiped out 10 enemies in Comet Rush mode.
Destroyed an enemy Creeper for the first time.
Passed 10 levels!
Lost in space 3 times...
Let's rock!
Got awarded with at least one medal on every level.
Destroyed the Vibemaster boss.
Destroyed any enemy with a rocket.
Destroyed a G-noid's turret.
Passed 20 levels!
Passed 30 levels!
Passed 40 levels!
Passed all game levels!
Used every power-up: Berserk, Magnet and Invisibility.
Failed to complete a level in 20 attempts.