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