I personally think that this would be the easiest brute to get the achievement on. You hopefully have upgrades to some guns and your stasis module.
You will be in a large rectangular room at the very tell end of the level (comes after fighting a large number of guys on the two catwalks above this room.)
There is a BLUE STASIS container in the room. When the brute attacks, launch the container at it. He will now be frozen for what seems like half a minute(exact duration of container unknown to me)
Using the detonator mines, launch them at the brutes feet. should take 6-8 mines without upgrades and 3-4 mines fully upgraded. either way this brute can be killed before it regains movement. if it does come out of stasis, one blast from your stasis module should give you enough time to launch the last mine(s).
alternatively: use 4-5 contact beam shots to one arm.
should work great, however if you NEED to give a negative vote, please explain your reason, so i can post better solutions in the future. Thanks