For this you need to play ranked domination with a friend and all 20 kills must be done in one match.
Once the game launches, get 10 brown, 5 red and 5 green minions, put a guard marker for all 20 minions right outside the steps of your spawn gate. Immediately run to the other overlord's spawn gate. The other overlord in the meantime as soon as the game starts, should be making his way to where the minions are, at your spawn gate. Once there they will start attacking. You should now be at the other spawn gate, this will prevent the other overlord spawning at his gate so he will always spawn at your gate and get immediately attacked, there is a period of invinciblility but should be plenty time to get all 20 kills before the 10 mins are up. I got the 20 with 1 min to spare. Once the achievement pops quit the game and repeat with your friend now doing the above.