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