You will find elite soldiers naturally by just playing the game but if you want to get this out the way earlier all you need to do is gain heat (fill the two bars next to your map on the bottom left of the screen) by killing soldiers and blowing things up.
Now the easiest way to do this is get a tank and drive down a main road. While driving shoot all the enemy trucks you see with
which will be your main cannon. Blowing the trucks up will build heat and when you gain enough heat you'll attract the attention of the elite soldiers and the game will tell you that they have began looking for you.
As the soldier show up (they normally drive up in trucks) just shoot the trucks with
using your cannon and if you see others running around use
to shoot them with your gatling gun as your main cannon reloads.
Using this method it took me about 5-10 minutes from the time I got into the tank until the time the achievement popped. I did this while driving around the main road clearing out checkpoints for the