Here is the full list of all 21 MOTHERGUNSHIP trophies - there are 2 bronze, 11 silver, 7 gold and 1 platinum.
Build a gun that uses over 20 parts at once
Die from lava damage after killing a boss
Craft a gun with DPS of over 100
Complete a mission wihtout missing a single shot
Complete a mission without killing anything except the boss
Complete mission without taking any damage
Complete your first mission
Unlock all trophies
Kill 1000 Spinbots
Kill 5 mobs in one shot
Survive 30 challenge rooms
Get 40 jump power ups in a single run
Take 4 diceroll rooms in a single mission
Fire 65535 shots
Complete nightmare mission without equipping any gun
Complete the campaign
Finish 1000 enemies using your fist
Add part to a gun 1000 times
Equip 10 armor upgrades
Find 15 secrets in a single mission
Reach room 20 in Endless