Here is the full list of all 22 Boom Blaster trophies - there are 4 bronze, 9 silver, 8 gold and 1 platinum.
Unlock all other trophies
Finish the tutorial
Finish the first level
Finish chapter 1
Finish chapter 2
Finish the game
Get the rocketlauncher drone
Destroy 10 harmless repair-bots
Purchase your first upgrade
Purchase 10 upgrades
Purchase all upgrade in one section
Destroy 100 enemies
Destroy 300 enemies
Get the triple shot for the first time
Get the double shot for the first time
Get the rocketlauncher for the first time
Get the flamethrower for the first time
Get the goose plasmagun for the first time
Shoot for 3333 times
Die for 72 times
Collect 15 health packs
Collect 10 grenades