There are 4 basic rules to follow to make this achivement as easy as possible.
1. upgrade/dual wield pistols (and your SMGS if you are so inclined) the damage upgrade as well as the armour peircing rounds help with brutes.
2. headshots. When taking out the mascot enemies, simple heashots with your upgraded pistol will dispose of them quicker and they wont be continually making you lose health. YOU DO NOT HAVE HEALTH REGEN IN THIS ACTIVITY so conservation of health should be a main priority.
3. Play with a partner. Having a friend along will allow you to clear out areas quicker and have your back in the harder areas of the game area.
4. TAKE YOUR TIME. As your health does not regen its a good idea to take it slow through the begginging of the activite getting headshots and looking up for snipers/health/ethical posters. these things will increase your score and allow you to finish without having to worry about killing brutes for points.
*brutes are like hydras. kill one, two more show up. it's NOT nessercary to kill every enemy inside the minigame to complete it. It's better to avoid brutes altogether if you can. (diving over the barricades so the melee brutes cant get you is a good tactic, also, unlimited grenades help)
**If playing with a friend BOTH OF YOU DO NOT NEED TO REACH THE END! only one of you need make it to the end, so if you have faith in your partner when the brute is spawned, have him hold his attention while the other player rushes forward to the end.
have fun :)