I didn't want to use up my spirit emblems on the brown ape since I needed them for the headless ape though. Just basically had to run around the arena to create enough separation between the two to get brown ape to attack me maybe 3 times so I could parry them and then get in a swipe or two. Lucky his health is pretty low but I just had to get quick hits and run, made the fight take forever.
Oh thank god there isn't a third.