So the best way I found to cheese this cheevo is by running behind this block as soon as I got into the room. It not only provides cover for the blue projectiles, but also makes the mutants unable to reach and melee you, while providing an opening to shoot with the pistols (the shots will not always hit the enemies, but they will if they get close at your left or far at your right relative to where Lara is facing in the pic).

It could be better if you get behind the block exactly in the position showed in the pic because if you get too close to the block, the blue projectiles sometimes can reach and damage you or even the mutants can hit you using melee.

Once you are in that position, TRY NOT TO MOVE FORWARD OR BACKWARDS (but you can rotate in place, if using tank controls). The janky enemy AI will make them run all over the room trying to reach you, sometimes they will attempt to shoot the blue projectiles, sometimes trying to melee you but if you are in the right spot, that shouldn't be a problem (you can also crouch behind the block if you think a blue projectile could hit you). Also, they will repeatdedly get in your sight to lock-on and shoot. It will take a bit of time but with patience, it's not that hard to get this cheevo.

Protips: since the time Lara will lock-on to the enemies is pretty short, try to mash the fire button instead repeatedly of holding it down. That way, Lara will shoot faster without the "cooldown" between shots.
Also, once you kill one of the mutants, you can save the game in case you have to reload because you got hit while trying to kill the remaining ones and it will still count for the cheevo.