There are several techniques that can help to decrease the effects of heart beat movement while shooting, and they are not only the purview of uber elite snipers on movies. A LOT of serious shooters, competition shooters and general advanced shooters know and use these. Small and large bore prone and BR taught and allowed me to learn and practice many of these.
1. Padding: Use heavy clothing, shooting pads, jackets etc between your shoulder, hand etc to reduce/eliminate the transfer of heart movement to the firearm.
2. Sling usage: A proper shooting sling can greatly help in reducing pulse beat transfer to the firearm by reducing the pulse pressure to the weapons forearm during prone positions without a bipod. A padded glove mitt etc also helps.
3. Recoil pad: There are recoil pads that are better at dampening pulse beats from the shoulder than others. Coupled with a padded shooting jacket, pad or shirt, it can greatly decease the transference.
4. Breath and Body Control: As already stated, study, learn and practice proper breathing techniques related to the shooting sports. There are numerous articles online: NRA, Mil, BR etc. Raise your upper chest and practice varied leg/body positions to be comfortable and reduce muscle stress.
5. Minimize Body Contact: For BR and some prone type shooting, many of us utilize a minimum contact approach with light stock to shoulder contact, no cheek pressure and no hand contact on the pistol grip. Only a light thumb on the back of the trigger guard and trigger finger tip on the trigger shoe. Gently squeeze.
6. Avoid Stimulants / Heavy Meals Prior: Avoid ALL stimulant drinks, foods and heavy meals etc prior to precise shooting. Especially prone. Extended stomachs lying prone press against the diaphragm and digestion raises heart rates and BP.
7. Between Heart Beats: While a little more difficult to master, many competition shooters have learned to use this with some success. When I was much younger, slimmer and a runner, I had a heart rate between 50-60, and with some practice, I could lower and "time" my trigger breaks while shooting in small bore prone matches. Over years, I spent more time on other effective ways.
8. Stay in Shape: As above, slimmer bodies with good cardio will lower heart rates and help.
There are several good online websites, books, and training seminars on improving (reducing) your heart's pulse effects on aiming and shooting.