I'm known as a very good offhand shot, blessed with good motor control and hand-eye coordination, but practiced for over 50 years. I literally wore out three Daisy BB guns before turning 14, two pumps and a lever. I'd burn off 10 tubes of Winchester BBs a week, all offhand. As an adult, I've shot in lots of offhand turkey shoots and shot numerous woodchucks and other varmints offhand out to 200 yards; deer, several yards beyond that. On good shooting evenings, I've shot 1/4", 5-shot groups offhand at 50 feet with my sporters.
I've shot with people who have equal or better hand-eye coordination than me and it seems to be a key to good offhand shooting. Some people can't hold a gun steady, no matter what they do. Those folks may have greater need for slings and bracing against their hip, ribcage, etc, more than people whose bodies can hold steadier. Practice is the real key to better offhand shooting. I practice offhand holding, but don't dry fire most rimfires without an empty shell in the chamber.
When shooting .22 sporters offhand, I can tell whether it will be a good session or not. If I'm not at peak, I resort to resting my left elbow against my chest a bit and that helps. However, when I'm having a good day, I can control the muzzle better with the left arm fully extended. Target shooter positions, especially resting the left elbow, are best for long strings of shots, but inhibit free movement when plinking at multiple targets and shooting moving game.
A key to better offhand accuracy is to focus one's attention on the center of the target and let the sights seemingly "wander" toward it, guided by peripheral vision. As the sight picture gets into the "acceptable accuracy" zone, the trigger is pressed smoothly, but if it wanders away, held steady, then pressed again as it approaches center.
Normally, I fire the first time the sights enter the target center zone, since I'm conditioned to do so, but also condition myself to hold for a second shot, whether it's taken or not. That is called follow-through and is particularly important for pistol shooting and rimfire rifle shooting because the bullet takes longer to leave the barrel than with faster cartridges and any let-down can throw a shot.
I tend to breathe regularly until just before the shot, when I often hold it for a few seconds. If shooting more than one shot, I don't pay attention to breathing, but do so normally.
A relaxed, upright position is most comfortable to me. I'm not turned 90 degrees, but part way, with my feet separated comfortably, my left about 4-6" ahead of the right. Right elbow is comfortably down, not forced, left elbow either straight or bent as comfortable at that time. Comfort is the key to good offhand shooting and I may hold a bit differently as fatigue sets in during a long shooting session...whatever feels the most comfortable at the time is the way to go.
Tension causes stress and shakes. If you feel shaky or your back starts to hurt, step away and take a break. Sit down, relax, and go back in 15 minutes or so and try again. Note: Caffine and good offhand shooting don't usually go together.
Don't make shooting into a chore, it shouldn't be, it should be relaxing and fun!!! It has been excellent for stress reduction, since it forces a person to concentrate on the task at hand and to put aside worries and frustrations of the day. Offhand pistol shooting is particularly good for stress reduction.
Hope this helps.