So often we have threads concerning equipment that it is refreshing to have one that deals with the mechanics of shooting.
While many target rifles are too heavy to shoot well off hand, this is not universally true. Still, a heavy rifle induces fatigue faster than does a lighter rifle and fatigue is the limiting factor when shooting off hand. The fastest way to bring on fatigue is to fight your natural wobble, a wobble that is magnified with powerful optics by the way. The fastest way to overcome fatigue is to accept the wobble and learn to fire your rounds quickly.
I do not shoot competitively, so I am free to pick my range, time, target angle, and the number of rounds I fire. Most often I fire two rounds. I simply shoulder the rifle, achieve my sight picture, put my finger on the trigger, and press. At the shot, I work the bolt as quickly as I can, reacquire the target and repeat for the second shot. If I can place each shot within 2" of one another at 100 yards and within 2" of my POA, I'm quite pleased with myself; sometimes I can, but not always.
But what is required to make a good off hand shot? Certainly your position must be as stable as possible, and the most stable position must take your natural point of aim into consideration. Begin by taking a boxer's stance towards the target. Your support arm must be directly below the barrel to limit any unintended windage error. Your firing hand assumes a strong handshake grip on the stock and the butt finds the pocket inboard of your shoulder. The rifle must be brought into your line of sight, rather than dropping your head to find the sight. When you have your sight picture, relax, close your eyes, then open your eyes to see if the center of your sight wobble has moved off target. If you are to the left of the target move your rear foot left slightly if you are to the right, move your rear foot to the right slightly to bring your sight on target. If you are too low, bring your rear foot slightly closer to your front, and if too high move it slightly farther away. Make all position adjustment in small increments.
Now that you have established a stable shooting position, you need to breath for each shot. If you find that you are running out of air, breath and start over. Much has been written on the proper aspect of breathing for optimum marksmanship, but it comes down to two schools of thought, the first which demands that the lungs be totally empty of air at the shot and that which suggests that the shot be taken at the natural respiratory pause. Those following the first approach claim that your position, particularly prone, is more repeatable from shot to shot than when shooting from a respiratory pause. I like the second approach better. I can shoot faster, because the shot can be made before I have forced all the air from my lungs, and my brain is not clouded by a lack of oxygen causing me to loose focus. As for position consistency, the natural respiratory pause is always with the same volume of air in the lungs, so any inconsistency to the position is purely theoretical and cannot be proven in practice. There are champion shooters who use both systems, but shooting on a natural respiratory pause is easier.
The wobble! If your sights are jumping all over the target or in some cases off the target, making the shot before you run out of air is an intimidating prospect. But this might help, and you can practice it with dry fire. When the wobble brings you onto the bull, or close to it, strongly tense up your stomach muscles. This is a direct violation of the rule that says you must relax for each shot, except that your mind and body are relaxed, just your stomach muscles are tensed momentarily. The effort produces an effect which might be recognized as a momentary brake. The wobble for that moment in time freezes in position allowing you to make the shot, if the brake occurs when the sights are on target. It requires some practice to master, but try it and see if your scores don't soar; 6s and 7s become 8s and 9s while 8s and 9s become 10s and Xs. If you find it doesn't work, trying it has cost you little and you can go back to steadily increasing pressure on the trigger as the sights cross the target.