How do I effectively fight Brutes?

Solution 1:

So far all I can do is run and gun (emphasis on run). The sniper rifle can do significant damage with headshots, but I rarely have the presence of mind to change to it in the middle of a fight (and it is often disabled in a diversion).

In short, keep upgrading your guns and hit them with your heaviest stuff. You can also try phoning Oleg as he is a physical match for them.

If you can blow up the truck carrying them, you can do significant (sometimes fatal) damage to them if they are still on it when it blows. Next to it doesn't seem to be as damaging. Even if it doesn't kill them, on escort missions they may not run up to you in time if you take out their ride first.

Solution 2:

Rocket Launchers and Grenades can help. Picking up a brute's mini-gun helped TONS. I usually use pistols... and you can get them upgraded/dual wield to very heavy damage unloading clips right into a brute's head.

Also you don't HAVE to run up to them and execute them, you can just keep shooting till they die. It was a long time before I figured that out.

Another thing that has been helping is using the Run key + jump when they get close, even if you don't manage to jump out of the way, you are already hitting the key that invokes the 'cut-scene' style evade.