You will be introduced to the Brute enemy during your mission on Palaven. This is the first main story mission after visiting the Citadel for the first time. As you are killing husks with a turret defending a barricade, your next fight will be against this monstrosity. Wear down the armor first, and try to avoid the husks that are also attacking. When you get it to 1 bar left, wait for it to charge at you. When it does, shoot it with your most powerful power or weapon. If it dies and isn't charging, you can try to let the husk enemies finish you off so you can restart the battle. These also appear online in the later waves if you miss them all in the campaign.
The brute I got this on (on Palaven) wasn't even charging me directly. He was going for a squadmate. Guess it doesn't really matter who they're after as long as you get the kill while they're charging.
This is not that hard, find a fight with a Brute (make sure you have room to manuever) take him down to a few bars, piss him off and shoot him in the face as he runs towards you. I got it with the Mantis sniper, was able to shave off the last 2 bars in one shot on Priority: Pavolon
If you miss the chances to get this early on, I recommend Tuchunka en route to the shroud. You'll have a few to deal with here with a long battlefield that's wide enough to evade them if they get too close. Make sure you're using the full length of the field and you should be able to time this easily.
There's LOADS of Brutes on the final mission (Earth) so don't worry if you haven't got it by then. I think there's 4 at once in one of the very last waves of the game. SMDH if you don't get this in one playthrough.
Yeah, this finally popped for me last night during the final stand on Earth and I was facing down four or five brutes at once. The one I took down wasn't even charging; he was just standing there after having charged one of my squadmates. When I took him down, I got the achivement. Really weird, considering that I had previously killed brutes that WERE actually charging me, with no achievement. :-/