This Achievement unlocks upon completion of Act 5 of the story when played on Assassin difficulty.
After you fight your way through the office building, Brummel really isn't too tough a boss to defeat. Start by moving from cover to cover and take out the hooded henchmen until you reach the doorway when Wesley says he'll have to take Brummel down from here. Brummel starts behind cover on the right side of the room and will occasionally move to cover in the center or even less frequently, to the far left side. If you've lost sight of him, just stay behind cover and watch for his arm to poke out and shoot at you.
You'll need to curve a bullet around the cover to drive him out of hiding - if you don't have any adrenaline banked (red bullets in the upper right, but you know that by now), don't worry; the game will spawn a couple hoodies on the catwalk above that you can easily take out to regain adrenaline.
When you drive him into the open, use single shots to the head, pacing them so that you hit him right after he finishes his hit reaction on each shot. Don't unload like crazy, as shots that hit him while he's reacting don't seem to do much. You can usually get about 5-6 good hits on him before he stumbles back to cover. Rinse and repeat until he's down.
Watch for the hoodies that drop close to your position, as they'll come right through the doorway and flank you if you're not careful. They tend to show up more frequently if you are low (or out) of bullets.
After a brief cutscene between Brummel and Wesley, you'll still have to escape the burning building before the level ends and you earn your Achievement.
If you have not already unlocked it, you will earn the following Achievement at the same time this one unlocks: