I like to approach shooting as I would any athletic event. After all most of are shooting bows heavier than most Olympian archers. I see many shooters that have a sag in their abs when they shoot. I'm talking about a little fat, I'm talking about pushing or relaxing their pelvis forward when they are at full draw. Essentially putting themselves in a weak position to shoot from. I personally set my lower back/abs in the pre draw phase of my sequence to eliminate the sag. I feel stronger in my shot and I believe I get better results doing so.
It also helps to work you core muscles when you do work out.
I believe the core is the most important muscle group to work out.