In my mind I visualize a wave of calm and focus that starts at my heart and flows down thru my arms then hands. Symbolizes my mind lowering my BP and pulse and breathing and calm.
My head (cheek), eyes, and arms are sort of this triangle I become keenly aware of, and want to make sure it has been stabilized and braced as well as I can so nothing is floating in space.... elliminating all the movements of "You" out of the picture as fast as you can, then immediately begin to focus on nipping in the bud the bodies adrenalin reaction and focus on slowing things down.
I (usually try to) remember to get my knees spread apart so that upon breathing my bit of belly won't push against my legs and thus cause my torso to rythmicly move back. Then... in my mind's eye, I'm visualizing the location of his heart and lungs and their position within his body, and me honing in on landmarks upon his body which help direct me to where to aim, such as his seeing his opposite leg to then know where his opposite shoulder is, when the shot is angled in.
Once I've got the crosshairs good enough I grow heartless and stone-cold and everything focus-wise shifts toward keeping those crosshairs from moving at all when my trigger finger begins to pull, attempting to increase the force on that finger in the most linear fashion as possible, imagining like my finger was a piece of robotics. All the while the pull is occurring... it's like I no longer exist where I am standing, instead all my focus is "out there" on him. Especially since during the pull he could move and you might have to re-acquire target point. I could probably have a damn bug crawl into my ear and I would not budge until the shot has been made. I want him that damn bad.
It's interesting with making a shot at game in the heat of the moment... it's kinda sorta like the same process you do when controlling your fears like when you go for a big jump on a Dirt Bike... reeling back in the panic. Only... you're instead electing to go the opposite direction a little more and subdue and control your bodies calm... rather than invoke a heightened state of readiness to react and make corrections mid-flight after launch.
Focus on eliminating all possibility of movements of "You" out of the picture as quickly as possible via proper positioning and placement of your body parts. The need to do this should be readily apparent to you from how you see your crosshairs jumpin all over the place until you get it right and locked in. Sometimes it involves making the decision to risk taking a few steps over to a nearby tree trunk or stone to rest it upon.
EDIT: And if using the shooting sticks, always making sure to also loop a finger over the barrel right there where your thumb is in front of the pivot-point on the sticks. And giving a little bit of pull-back pressure to not only ensure the rifle is in your shoulder pocket, but also so that this barrel holding arm/hand/finger is kinda locking the barrel down and into the pivot point of the stiks. And all that is now rock-solid and not moving... then hurry-up and make your fine tune adjustments in the crosshairs, especially such as when doing Ground Squirrels, since they're so small at distance. Also quickly judging if you'd be served better by bothering to fuss with cranking up the magnification on your scope in that moment. Sometimes with the little critters it's a darn good idea to possibly go up to like maybe 6x-7x if they're, let's say.... greater than 70yds or so? Sometimes ya just can't though, like if it's getting dark...you just might be forced to leave it on 3x right there toward the end of legal shooting light, just so you can gather enough light to see good enough thru it to aim properly.
Most visualization and repetitive mantras happen only on the range and practice. Shots are too quick in reality to go through all that. Needs to be baked in.
Same for any weapon for me. My first thought is breath and try to calm down. From there its form and breath. Then pick a spot and breath. Then squeeze. That is all if I have time like the animal is walking in or I am stalking. Quick scenarios I jump to aim and squeeze.
Clip - is the d-loop where it needs to be relative to peep
Grip - is my bow grip where it needs to be for min torque
Draw - remember to draw with rhomboids
Jaw - Find my precise anchor
Yaw - Level the bubble
Center- the sight in the peep
Float - Observe the float and get comfortable with the boundaries of float, otherwise let down
Flight - Keep the pin on target all through the flight
Clip (release on D-loop)
Grip (centered on thumb pad with fingers relaxed)
Raise (bow arm keeping shoulder low and elbow rotated in)
Draw
Anchor (valley between index & middle knuckles cradling rear corner of jawbone)
Center (sight housing within peep)
Level (sight bubble)
Float (pin over the target)
Squeeze (slowly bring thumb and pinky together to trigger release)
Hold (steady until the arrow reaches the target)