What kind of physics is this exactly...?

A type that deals with movement and energy expenditure…

It is used in calculations by bio-mechanists (those guys that study the mechanics of motion in sport).

I can’t exactly pinpoint what I’m trying to say (b/c then I wouldn’t have to ask)…

Let’s suppose that I want to calculate the punch that has the most force - taking into account all the details (angle of hand/wrist, area of target, orientation of legs, energy used during release).

What kind of physics (or principles relating thereto) would I be using to calculate the force and the overall efficiency of the punch?

It wouldn’t come under any of the other sciences - it is more physics based.

I was thinking classical mechanics but that doesn’t take any account of energy transfer inside the body (say how potential changes to kinetic etc.).

Do any dopers know? I may end up pursuing this as a hobby - and I’m real interested and would prefer to have an equivalent field to study.

Just a note, the point of physics is that it applies generally to all objects. But you need to have a good model to get good results. You can model a punch with or without energy transfer inside the body and get different results, but in both cases you’re using classical physics.

You do need to know something about the body in order to model it using physics, however, and there are specific fields of study pertaining to that. Physiology is the study of the body structure, which is what you’d need to model the body. Exercise physiology covers some of the elements of motion, but also includes factors such as nutrition. You might also want to consider kinesiology, the study of movement, but it’s a bit broader(definition here). In fact, biomechanics as you mentioned is exactly the right field for applying physics to life forms.

I think you are looking for “dynamics”.