Here is the full list of all 37 Attack of the Earthlings achievements.
Complete Mission : Improbe-able
Complete a mission 10 turns below the target par time
Kill another enemy with the Banshee Death Explosion
Destroy the Blood Samples in Mission : Improbe-able
Free The Matriarch in Mission : Improbe-able without losing a grunt
Complete Dead End Job
Consume 500 Biomass (over any number of playthroughs)
Release the Rogue Motivatio in Dead End Job
Complete It's My Birthday And I'll Die If I Want To
Kill the Overseer in It's My Birthday And I'll Die If I Want To
Complete Serial Drillers From Outer Space
Successfully pull off a Group Attack
Complete The Fast And The Luxurious
Complete I Purge You To Reconsider
Complete the Game
Kill both Barry and Paul in I Purge You To Reconsider
Kill all the Executives in The Fast And The Luxurious
Complete The Fall Of The House Of Pecker without any Mutagen Upgrades
Complete Dead End Job without losing any units
Complete The Fall Of The House Of Pecker without killing a single enemy
Complete Serial Drillers From Outer Space in 11 turns or fewer
Complete Dead End Job in 21 turns or fewer
Damage Paul with his own Mines
Lure an Enemy into the path of Dickinham's mech in Mission 07
Deal 200+ DMG with one group attack to a single unit
Kill 5 enemies with one group attack
Kill a unit through a wall with Ground Pound
Lure an enemy onto a Trap
Move 18 tiles with a single unit in 1 turn
No one tells Carlos what to do
"As Designed"
Never question John's sense of duty
That'll fool 'em
One day this will work
You get what you pay for
... You really didn't achieve much
Kill 100 Galactoil Employees (over any number of playthroughs)