This achievement is for killing 20 desolator troopers in one game, it is not cumulative, once a game ends your count resets to 0, which means there is only one mission in the game that can give you this achievement, that mission is called Kill-A-Ton.
Map Area where the mission can be found: Central Eastern Australia (southeast of your television screen for those who suck at Geography)
Play as the Rising Sun and set up 4 refineries, two in your base and two to your immediate east. Build a mecha bay, and build 5 tengus as preliminary defence. Now upgrade your mecha bay and spam VX choppers. (If you haven't played as the empire before, you need to press rb+x when your VX chopper is selected to make it a useful ground attacking unit instead of an anti-air unit.)
Now build another mecha bay which you won't bother upgrading, but will use to spam tengus which you will put into flight mode (rb+x when selected) to protect your VX strikers from the Russian migs.
When you have a minimum of 6 tengus and 6 VXs, scout the map for desolator troopers (they're just walking around, often near the cliffs with the abandoned super reactors on them).
Don't even bother attacking the Soviet base, just fight off migs that come for your VXs with your tengus, make sure you're continuously building more tengus and VXs back at base, whilst you wait for the Soviets to send more desolators at you. If the Soviets send a Kirov airship (big blimp looking thing) be sure to dispatch your tengus to deal with it as that can easily destroy your base before you get your 20.
They will keep sending desolators across the battlefield towards your base, so at this point its just waiting for them to send enough desolators for you to pick off. Sometimes they'll send a group of 4-5 desolators all at once, so this won't actually take as long as it sounds. I estimate you'll get this achievement within 10-15 minutes.
Once you kill 20, the achievement immediately pops, you don't need to finish the mission to make it pop, so once it pops you can feel free to quit the battle.