The easiest way to do this is snipe him.

Make sure when you go back into the jungle, you pick up one of the beam rifles from the jackals, and pick up the sniper rifle from the crashed pelican.

Then, when it shows the video of the brute throwing Sgt. Johnson into the the room where you free him, first take out the snipers, then start sniping the brute from the place where you see the video.

But make sure you keep an eye out for Covenant shooting at you. Enjoy!