The minigame is 10 waves of tanks in a top-down 2D twinstick-style. Each wave has an increasingly large number of tanks to destroy, and at wave 10 there will be an infinite number of respawning T34 tanks and the final boss, a Maus.
Sometimes when you kill a tank, it will drop a box. This box is a powerup and includes things like homing missiles, cloaking, speed boosts, and perhaps most helpfully, a health restore. I'd recommend holding on to health powerups until you need them; later waves can get hairy, and you do take powerups from one wave into the next.
I got this achievement on my very first try by simply going around the battlefield in a circular motion. The enemy tank shells travle very slowly, so by keeping on the move you will be able to dodge most of them. Just keep your reticule on enemy tanks and hold down the fire button. If you disable a tank, you can easily drive behind them; hitting an enemy from the sides or back does 2-3 times as much damage as from the front, so prioritize any disabled enemies. Do not let yourself get surrounded; I very nearly died on wave 8 by getting too brave and allowing myself to have three tanks around me.
The final boss is not that hard. The Maus' shots travel very slowly, just like all the other enemies, so if you stay on the move he will likely miss most of the time. The major difference between him and the other tanks in the game is that he has a lot more health and his shots do more damage. The T34s are very easy to kill and they will drop powerups; any time you drop below 2/3 health I'd recommend focusing on a few T34s and hopefully getting some health. Even if you don't get health, cloaking will help immensely as enemies will stop firing and even stop moving until your cloak wears off, allowing you to kill more T34s and hopefully get health from them. Make sure after you kill the Maus that you don't get ganked by the T34s, who will still be on the field shooting you for a few seconds after the Maus goes down. If you die in these few seconds, you won't get the achievement and will need to start all over again.
Overall this is not a difficult achievement, I assume most will get this relatively quickly, probably even on their first attempt like I did.