Here is the full list of all 13 Super Destronaut DX achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Reach 1K in Hardcore Mode
Complete 12 challenges
Reach 10K in Time Attack Mode
Complete 6 challenges
Complete 3 challenges
Complete 1 challenge
Reach to 100K points in Classic Mode
Reach to 25K points in Classic Mode
Reach to 50K points in Classic Mode
Kill 1 special red enemy
Die once
Hit one of the grey enemies
Kill 1 enemy