Diffrent Tactic here, we tried a lot and (maybe because our Healer (me) was only 31 on our first evening) we figured this out:
We had Jugger-Tank, Marauder DPS, Assasin-DPS and Operative-Heal
Marauder + Assasin took the Chief (who provides the shield) to the door where you can exit after the encounter. That way the Shield is broken and both meele-dps and the healer are out of range for the AoE of the Commander. With Kolto-Probe and Surgical thingy healing the tank was quite easy and I only took one or two grenades instead of 4 in a row.
After the Chief is dead, burn down the Commander, Tank kicking the Medic
Well, with the medic last man standing it should be easy to figure out
Worked with diffrent Partys 5 times.