You and I do -- Rifle 4 and Flamethrower 3. Stack toughness via adaptive armor. Drop in two turrets to distract the Eater of Souls. Auto attack with rifle until the bar turns blue then hit 4. Swap to Flamethrower and auto attack until the bar turns blue, then hit 3. Swap back to rifle. Rinse and repeat. Medic Gyro as needed. I literally stood still for the entire boss fight. Burned him to the ground in less than 2 minutes.