Here is the full list of all 37 Blasters of the Universe trophies - there are 24 bronze, 7 silver, 5 gold and 1 platinum.
Near-Miss 10000 Shots
Kill 5000 Swarmers
Block 100000 Projectiles
Kill 5000 Troopers
Kill 5000 Flying Drones
Kill 1000 enemies while they are jumping
Dissolve 100000 enemy shots
Get 1000 Reflection Kills
Get 1000 Headshot Kills
Kill 100 enemies while they are jumping with a bounce shot
Get 1000 Bounce Kills
Score 500000 points in the Core
Score 1000000 points in the Core
Score 250000 points in the Core
Score 1000000 points in the Passage
Score 500000 points in the Passage
Score 250000 points in the Passage
Headshot kill an enemy with a reflected headshot
Find Alwyn's Video Rental Card
Headshot kill an enemy with a bounced headshot
Stun 1000 Enemies
Score 1000000 points in the Facility
Score 250000 points in the Facility
Score 500000 points in the Facility
Score 500000 points in the Barrens
Score 1000000 points in the Barrens
Score 250000 points in the Barrens
So you beat the game
Kill Alwyn, Virtual Space Lord
Kill the Protect0r Boss
Kill the Spect0r Boss
Kill the Destruct0r Boss
Point the laster pointer in Alwyn's eye
Unlock all trophies
Kill 2500 Chargers
Kill 1000 Heavy Gunners
Fire 500000 shots