Here is the full list of all 37 Alien Robot Monsters achievements.
Build 50 towers
Gain 10 stars
Field 256 marines
Stun 384 robots
Destroy 100 robots in melee
Field 64 marines
Gain 20 stars
Destroy 50 robots in melee
Field some space marines
Start your colonization of Planet X
Defeat Forest biome boss
Defeat Wasteland biome boss
Defeat Swamp biome boss
Defeat Mountain biome boss
Defeat final boss
Complete all Planet X levels
Save the natives
Fire 256 sniper rounds
Destroy 100 robots with snipers
Use 1337 hand grenades or mortar rounds
Fire 500 missiles from orbit
Deploy 32 reinforcements
Deploy 128 reinforcements
Build 200 towers
Build 400 towers
Build 800 towers
Gain 30 stars
Gain 40 stars
Gain 50 stars
Gain 75 stars
Gain 90 stars
Gain all 111 stars
Destroy a robot with native arrows
Destroy 128 robots with fire
Destroy 99 robots with satellites
Destroy 128 robots with Atomizer
Instakill 50 robots