You will recognize Brutes, as they are clad in heavy armor and use shotguns or LMG's later into the game, while they slowly walk towards your position. To unlock this achievement, you will need to kill 10 of them with a melee attack. To do this, run up to them and press and you will start a confrontation, where you will have to mash fast to kill them.
Note: You can kill Brutes in melee without a confrontation by melee attacking them while in overkill. This will kill them instantly, without causing the confrontation and thus killing Brutes in this manner, will not count towards this achievement.