I practice something called diaphragmatic breathing.
Tips for diaphragmatic breathing that helps with managing adrenaline.
Try practicing these every day, and as a part of preparing for each shot.
First, place one hand on your chest and one hand on your abdomen. This will help you know that you are breathing with your abdomen and not your chest.
Slowly exhale through your nose by pressing your diaphragm(belly) down. A three or four count should be good. If the hand on your chest moves, you are not using your diaphragm.
Slowly relax your diaphragm and breath in through your nose. This will draw air into your lungs. The hand on your chest shouldn't move. Use a three or four count on your inhale.
Once your abdomen is relaxed, give your self and three could before you repeat the process and exhale again. Repeat it 10 times or so for daily practice. When you are hunting, start it as soon as you get that rush
That is basically it. That method does a lot to manage adrenaline rushes. It may feel odd at first and you may also feel that you are not getting enough oxygen. More than likely you breath using your chest. By practicing this regularly, you will learn to breath normally via your diaphragm. Though on normal breathing you will inhale by enlarging your stomach instead of pressing down. It can work wonders for day to day stress management.