Here is the full list of all 20 MOTHERGUNSHIP achievements.
Equip 10 armor upgrades
Fire 65535 shots
Take 4 diceroll rooms in a single mission
Complete your first mission
Kill 5 mobs in one shot
Craft a gun with DPS of over 100
Kill 1000 Spinbots
Complete mission without taking any damage
Complete a mission without killing anything except the boss
Complete a mission without missing a single shot
Survive 30 challenge rooms
Get 40 jumps in a single run
Build a gun that uses over 20 parts at once
Die from lava damage after killing a boss
Complete a nightmare mission without equipping any gun
Complete the campaign
Finish 1000 enemies using your fist
Add part to a gun 1000 times
Find 15 secrets in a single mission
Reach room 20 in Endless