Forget strength. it's about *stance*. Look at the petite female smallbore shooters hitting a 0.25" bullseye with a 12lb rifle.
You build your position from the bottom up. There are main schools of thought - combat stance and target stance. You'll probably use neither when hunting, but you can apply the principles:
1. You need a wide enough stance in your feet to support you and the rifle.
2. Do not lock your knees, you will start to tip and waver.
3. Get your weak hand BACK towards the action, toward the balance point. NOT way out on the forearm of the gun. The more extended your arms, the more you will shake. Your deltoids will fail very quickly.
4. Unless you're wingshooting, your elbows should be at your sides, particularly your weak hand, allowing the weight of the rifle to bear down your forearms (both of them) and into your body which is supported by your feet. If you don't, you'll be using your deltoids, which are very small muscles. Give yourself a break and use your core!
Your fall/winter clothing will insulate your arms from your heartbeat. You will need to control your breathing: half-breath in or out, then hold it. Shoot within a 3 count or breathe again. How long do you need to hold your position? If it's a rifle you can bring to your eye quickly (practice!), then you won't have to hold it long. When you're practicing, practice from a carry position. Do NOT shoot-shoot-shoot without lowering the gun unless you expect your quarry to shoot back. Practice follow-ups, yes, but don't stand there like a doof holding your gun until you shake. The FIRST shot is the most important.
Build your position from the bottom up: feet, knees, hips elbows, shoulders, head, sights, target, *bang*.
A target stance will generally shoot "across" the position. i.e. the feet will be 90deg to the target and you will fire across your weak shoulder. A combat stance will generally shoot "out of" the position, without the twist-up of the target stance. The principles above can be applied to both, or anything in-between. They also apply for kneeling and sitting positions, of course. Your body is the sandbag, settle into your stance, whatever it is. Oh, and if you have to scrunch up your shoulder to see through your scope/sights, then either the gun/sight combination doesn't fit you, or you're doing something wrong. You should be able to be *relaxed* when shooting on your hind legs.
-Daizee
Example of a target stance, shooting across (mostly) the position. Your forearm grip when hunting will likely be a little more... determined than here: