I suggest using a pistol, preferably the Spectre-issue one from either The Citadel Requisitions Officer in the lower portion of the C-Sec Academy, or your Requisitions Officer onboard the Normandy. Equip it with a Heat Sink and Tungsten bullets which are good against synthetics. Advantages of the pistol + heat sink + tungsten bullets are that you can fire more before overheating naturally because it's a pistol, with added shot capacity from the heat sink preventing overheating a bit, and tungsten bullets are good against synthetics.
The Spectre-issue pistol does over 200 damage, the same as any other spectre-issue gun (some do more, but overheating is much more as well) or a high-end standard weapon. Keep your aim skills high and shoot him repeatedly when he sits in one spot on a wall, and stop shooting with the red beam hits you as that will overheat your weapon if you fire whilst that beam is discharging. Continue doing this (you can also shoot him as he crawls along the ground if you're quick enough) and you'll hopefully beat him within 2-10 minutes or so.