Here is the full list of all 14 Robozarro (EU) trophies - there are 2 silver, 11 gold and 1 platinum.
Unlock all other trophies
Destroy 10 Mini Bots.
Collect 30 Junk.
Defeat the Sewer Boss.
Buy something from a vending machine.
Grab 20 objects with the Grab N' Blast.
Destroy 4 yellow doors in the Sewers.
Find the Robo-Claw.
Destroy 5 Sewer Turrets.
Throw a grenade.
Destroy 10 Robo Spiders.
Get your first blaster.
Talk to Fix.
Open 1 garbage can.