Due to the RNG of the map variations there are many potential chances to get this achievement. However i'd suggest it's easiest done on an incursion mission.
During the main campaign or after its completion you'll be given 3 side missions at a time. The easiest mission i found was the
"Aldair Incursion, Mission: Enduring Python" which will see you fighting through two sections to get to a supply box. In the first half of the mission (before you get to the halfway mark and open the gate to the second section) you will encounter a few drones, wretches and a Theron guard. Kill them all and collect his torque bow.
Move all your units to the gate and before opening it, have your torque bow unit at the front ready to go through, there's a LOT of enemies on the other side waiting for you. On a fresh turn, open the gate with a different unit and move your torque unit as far as they can forwardleaving themselves a turn to attack. Take along a second strong (tanky) unit.
There's a few ways pending on your luck that this can go. Either;
Run in first and find 4 enemies close together to get the element of surprise! OR, 3 wretches should run forward, hopefully with another unit (grenadier or Theron likely) and you might be able to land that quad kill. If not then there should be 4 snipers just ahead hiding behind a square planter. Don't worry about your units getting hit or potentially killed as you can restart from the checkpoint (just before you enter the gate).
Go for the first chance if you can, but if not use your tank as a distraction to soak up the damage and push your torque unit up so you can get a better angle on the enemies. Most importantly, DO NOT ATTACK ANYONE ELSE! Leave all enemies alive so as to get better odds on four grouping together.
If you didn't manage it, then just restart at the checkpoint and have another go!
See below for a video from the half way mark!
NOTE: Achievement didn't pop as i re-recorded the clip!