This may come naturally, but this is how I went about setting this up late in my run through this game.
I used Tournament 6 since there is just one arena. I re-rolled the tournament until it had a poison cloud.
My robot had the Camouflage augment so he could hide in forests. Unless enemy robots have a specific perk to detect hidden robots, they'll never see you.
Stealthily make your way towards the poison cloud and stay hidden so enemies will not engage you. You don't have to avoid all conflict, but I chose to. Keep passing your turn and staying in stealth and the enemies will eventually start to kill each other off. Once there is only one left, you want to get into the poison cloud and start taking damage- hopefully there are stealth tiles you can use. You take 1 damage for each step you taker in the cloud and you also take a point of damage if you start your turn in the cloud. You need to carefully manage your position so that you exit with one life (a teleport/jetpack will make this easier), then engage the final enemy.
The battle will be precarious since you cannot take any damage. Ideally, you'll have Attack Harmony along with Free attack and Free Defense Setup. If you can kill the enemy before he manages to get through unblocked damage (or uses a damage token), the achievement will unlock at after the ending screens.