Win62A, "Crabbing" is one of the techniques taught to shoot while moving at an oblique to the target, but you still have to use the approach that your torso is a turret and you legs acts as shock absorbers Erik states.
I may be pillared for this but I agree with the use of air soft, since most people cannot get simmunitions. But lacking that you still can practice on a square with your service weapon if you have some creativity and someone to assist
You are not shooting at the assistant either, what we do on the square range if we are doing live fire is we have a shooter and an AI move through an array of targets, the Marine under instruction is not allowed to flag any of the targets and when the AI calls a target the shooter has to ID the target and shoot while still moving at what ever angle he happens to be to the target.
God truly fights on the side with the best artillery