I went Bowhunting near Limpopo, S. Africa with my Uncle...I had to use a crossbow because an automobile accident left me with little muscle in my left shoulder and I could not draw a compound bow back properly.
We were not hunting, specifically, for a brown hyena. However, during our trip, we came across three different brown hyenas. The first came within about 15 feet of my blind, in broad daylight.
The second ran in front of a guide vehicle, twice, and got hit by the back tire (and killed) the second time it ran out.
The third came on a night hunt, when I was hunting for bushpigs (I know, not a huge trophy, but still fun to hunt). I was able to shoot the hyena from a slightly elevated 10 feet away. One bolt, perfect shot from front shoulder through the lungs and out the opposite shoulder at an angle.
The hyena let out the most horrendous yelp, ran rampantly through the brush for about 20 yards and fell over.
Although I wasn't specifically hunting for brown hyena's, this was definitely a blast to hunt. It provided for one for most exciting hunts I've ever been on.