The best way to deal with these fiends is to slowly charge toward them, and as they are about to let loose a shaft, quickly strafe to avoid it and just repeat that tactic until you get within melee range where the thrashing begins. Standing at range and picking off folk with their prissy little short-bows, these goons can be a right pain in the behind as they can inflict damage upon you whilst you’re off staving in the skull of some poor unfortunate.
Of all the various types of foe that can appear in the arena, the archer can be the most infuriating.