Here is the full list of all 12 Shoot Many Robots trophies - there are 9 bronze, 2 silver and 1 gold.
Beat a mission wearing the astronaut helmet and backpack!
Beat a mission wearing the baby carrier!
Reach level 50!
Kill 10000 robots!
Complete a mission on hard or insane without dying or drinking juice!
Punch two bullets, killing two robots, with one melee swing!
Get 75 stars!
Have someone you invite join you in an online game!
Destroy a robot overlord in multiplayer!
Come in 1st in a four player mission!
Revive other players 8 times!
Kill 100 robots!