A major component of success in shooting is psychological, though this page is about the physical side of things, which is also a very important component of success. The role of physical fitness in shooting will vary a little between the disciplines of the sport - for example the physical demands of pistol shooters will be different from clay target shooters. See out discussion of the Fitness Components for Shooting.
Generally, it is important to have great balance and coordination to be a good shooter, but you also have to be flexible to get the body into the correct positions comfortably, and in some disciplines it is important to be agile and quick. Muscle strength and endurance is also very important for holding the gun up and moving with control.
According to a poll of site visitors (shooting factors of success), the most important physical aspects of success of an Olympic clay target shooter are flexibility, quickness and agility. Another poll, which looked at just the most important Fitness component for shooting, Balance and Coordination is currently voted highest.