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
Reach 10K in Time Attack Mode
Reach to 50K points in Classic Mode
Reach to 100K points in Classic Mode
Reach to 25K points in Classic Mode
Complete 12 challenges
Complete 6 challenges
Complete 3 challenges
Kill 1 special red enemy
Complete 1 challenge
Die once
Hit one of the grey enemies
Kill 1 enemy