i have not been doing this for long so don't take this as sold ture but for me i have been finding that a slightly out of focus on paper targets has made it easier for me to keep the retical on target it is just something to try
as far as breathing i have found that if you can stay calm, not get exited, and clear your mind of all else the slow deep breaths come more ezaly
Everyone gets out of breath upon exertion, even marathon runners, so physical fitness isn't necessarily a viable option. Standing upright helps because your diaphragm isn't compressed, thereby limiting tidal volume. Another method mainly used in patients with emphysema/COPD is to use "pursed lip breathing." This is when you exhale with your lips partially closed, adding back pressure in your lungs. This increases oxygenation from the lungs to blood. Sticking to these two things will get you back breathing normally sooner and allow you to control your breathing however you want when you take the shot.
A shooter wants to have as little muscle tension as possible when firing a weapon. Because of this a shooter must establish a natural point of aim and FIRE DURING THE NATURAL RESPITORY PAUSE. Holding your breath actually creates tension in your body that can easily vary from shot to shot...which will kill accuracy since repition is the key to consistent shooting. Also, your eyes will begin to lose focus after 10-12 seconds when holding your breath. remember to exhale completly so your body is completely relaxed.
So the 10-15 second time period when your eyes have enough oxygen to focus sharply after exhaling COMPLETELY is the best time to fire a shot. Remember to check your natural point of aim, relax your body to avoid muscle tension, and to focus on your sights to maintain a good sight picture. Do not forget to slowly pull your trigger to the rear...apply steady, constant pressure throughout your squeeze...avoid jerking your trigger or varrying the pressure/speed at which you depress your trigger.
In the last several years, the top snipers are mostly letting ALL their breath out before squeezing the trigger, claiming better stability and fewer flier rounds because of it.
It makes sense to study yourself at different levels of breath-in-the-lungs at trigger time and check your groups. Do it again the next day in reverse order to see if fatigue was a factor. This is an exersize for the .22 that matches your big rifle, the decision coming long before hunting season.
As to staying in shape, if you don't, how you gonna haul all that moose meat out of the canyon?
I totally agree with firing the shot on the exhale. I have intentionally watched the scope movement while sighting in. On inhale the scope moves low left, on exhale it centers again, that is when I start to squeeze. The shoot, as I have been taught should almost surprise you when it goes bang! I seem to shoot tighter groups, more accurately when I shoot in this manner, I believe this was Army training but don't know for sure. That was a long time ago and things get fuzzy as I age
One more point to bring up is the magnification of your scope. If you are reaching out beyond 400 yards, you are probably up above 4x magnification. More magnification means more scope movement as you approach trigger time. If you are having problem with breathing movement, try zooming out a bit and getting used to aiming with less magnification. It may seem counter-intuitive at first, but stick with the idea for a while and see if your score improves. Backing off from 10x to 6x at 800 yards seems to bring down my group size, I'm about the same at 1,000 yards for 6x vs. 10x, and out at 1,500 I do better at 14x. It's an individual thing - some guys have dead hands and use 20x. My heartbeat is too powerful for 20x, but I still work at it to see if I can overcome my limitations.