After reading alot on this, being stuck there and cursing helplessly at th tv, I got it. It's not that hard once you know what to do.
Like many people suggest, kill those birds as priority numero uno. Run near one and Z lock it (hold Z), *THEN* hold B to pull out your bow. As soon as you release B you'll shoot an arrow and kill the motherf**** instantly (hold Z the whole time!). I was doing it the other way around and it's too hard to do in the heat of the action. You don't even have to aim with this trick. Do the same with the carriage and the bow. Target, *then* pull out your bow and release.
I almost break my disc in two before watching a video on youtube. The guy was able to insta-kill every birds on sight. I knew I was missing something.