It's "Link" again, and this time, he's got a bow, which makes him doubly annoying. Not only that, he likes to run away, a lot.
The best way of dealing with him is swarming him with Echoes and Swordfighter Form. You want to back him into a corner if you can and use Echoes as a distraction so you're not taking hits.
When he turns purple, he can fire multiple arrows at once. Keep wailing on him and you'll beat him, which will reward you with the Bow for your Swordfighter Form.