As long as you do not fire the sniper rifle, you will get the achievement. I did this on Legendary and simply gave the sniper rifle to Buck. For the most part, you are going to want to be Noob Comboing all the brutes for the first portion of the mission (and further if you don't find any other weapons.)
The layout of the mission means that a pistol with serve you better than a sniper rifle will anyways. If you have already completed the level on legendary then just run through on heroic, however if you have yet to complete it on legendary and are at least somewhat competent at the game, then play through on Legendary and get the level out of the way whilst also dealing with this achievement.
EDIT: While you cannot use the sniper rifle, you can use the Beam Rifle. Thank you to the people who have checked this.