The Tactacam is made specifically for recording hunting videos and it actually bolts onto your bow as the stabilizer. My buddy had an early model a few years ago and it worked well, I'm sure the newer ones are even better. it has zoom built into it so that you can see an animal as it comes in and it doesn't look like it is 100 yards away when it is really only 20 yards away like the gopro does.
If I had the money I'd buy the new Garmin Virb 360 camera, that thing is amazing. It captures 360 degrees of video. It automatically stabilizes all video so it doesn't matter if you hold your bow upside down, it will always show right side up. bow Shock should be tuned out as well, plus with 360 degree view it will capture every thing that happens around you including animals that come in behind you. Check it out, it is hard to explain how mind blowing that camera is! The only downside is it doesn't have zoom but maybe you can edit the video to look closer.