There is no time limit to scan the mission after receiving the alien ruler weapons, so this achievement becomes much easier to do later in the game when you soldiers are higher leveled with better gear so they hit harder and are more accurate. Bring all the alien ruler weapons you have as insurance in case you can't instantly kill it from an ambush. Gunners/Sparks/any class that strips armor with normal shots will also help. Alien Rulers story spoilers ahead.
*** Spoiler - click to reveal ***After you make your way past the room where you are ambushed by a lot of viper neophytes popping out from vents you'll notice an ice chamber where the Viper King will spawn. Save your game here in case you make a mistake. There is a certain point in the room where you trigger the viper king spawning. Move all but Bradford to the front of the raised platform and put all of those soldiers on overwatch. Now move Bradford forward to trigger the viper king spawning and hopefully all the ambush shots will kill it or sufficiently damage it for you to finish it off.
Alternatively equip as many repeaters you can onto your weapons and try to get lucky.