I have a friend who is a deadly shot with a rifle, on a target, but as soon as he sees live game, his shooting skills go out the window. Its an interesting mental game, finding what works for you to work through an adrenaline surge. There are a few ways people react to adrenaline, and figuring out how to work through your own responses, seems to be the key.
I've played a little mental game with myself for years, wherein I convince myself that hitting or missing really doesn't matter. If you think about it, most of the time these days, and certainly in my situation, its not survival on the line. That would up the ante a lot, if it were.
Instead, I tell myself from the start of the hunt that it honestly doesn't matter if I take the animal, or not. If not, the animal lives another day, and it wasn't its time. Or mine to kill it.
I found that putting "pressure" on the shot upped my chances of the arrow going where I didn't want it to. A soon as mentally it became "just another shot", I calmed right down, and it really was just another shot.
I guess I try to emulate what I do when I practice, right down to the mental state, because well... thats what we practice. Change that, and things get weird.
I don't have a large adrenal response either, though.