How do I defeat the CAT6 Heavy on Insanity difficulty?

I'm playing the Mass Effect 3: Legendary Edition Citadel DLC on Insanity difficulty, and I've met an enemy I can't kill: the CAT6 Heavy.

I've tried different combinations of squad, powers, ammo and tactics, and I can't take on more than one at a time.

Right in the beginning of The Citadel, you have 3 to contend with. The regular guardians have a simple exploit, and you can rip their shields from them with a biotic power. CAT6 Heavy has no way to remove their shield. The concussive shot momentarily makes them move their shield, but it doesn't make them any less vulnerable. Even hitting them when they are turned, and hitting their body doesn't seem to hurt them much.

I'm playing on Insanity difficulty, and I will not change the difficulty. I am playing with a Soldier Shepard.

How do I defeat the CAT6 Heavy on Insanity difficulty?

• Reportedly, the shield can be removed with Pull (but not Lash or Singularity), Overload, Energy Drain, and Sabotage. Energy Drain can be selected as a bonus power by any class once you have started the Rannoch arc, if Tali is still alive and you invite her to your quarters. If you have not yet started the Rannoch arc, then beginning Citadel may be inadvisable unless your class natively possesses one of these powers (Soldier does not).
• The shield has a "mailslot" like the one on Cerberus Guardians. If you can make accurate headshots, you can shoot right through it.
• At the beginning of Citadel, you're placed in a very unforgiving fight with several CAT6 enemies and given an M-11 Suppressor. This gun has a number of advantages and disadvantages:
  • It does good base damage for a pistol, and also fires at a decent rate compared to e.g. the Carnifex or Paladin.
  • It has the best headshot bonus of any weapon. Headshots do four times as much damage as other shots. Soldiers can use Adrenaline Rush to easily line up headshots and kill enemies quickly.
  • It is very heavy, and may significantly increase your power cooldowns.
• This fight has infinitely-respawning enemies. You do not have to kill them all (nor is it possible to do so). You have to get to Brooks and revive her.
• Because active powers are less useful, you may want to re-spec Shepard to focus on the class passive ability (Combat Mastery) and/or Fitness.