The best time to control the natural breathing cycle is during the "respiratory pause," which occurs when you're naturally done exhaling. One key here is to not force the air out of the lungs, but let it happen as naturally as possible. During the respiratory pause, the chest muscles are relaxed, and you can stop breathing longer without feeling uncomfortable. If you try to stop breathing while your lungs are filled with air, you'll begin to experience muscle discomfort sooner than if your lungs are mostly empty and the muscles involved with breathing are relaxed.
How long can you extend the respiratory pause? That depends on your physical condition and state of mind. This is why training to increase your aerobic capacity is important to your shooting success. For most people, the respiratory pause can be extended for somewhere between 8-10 seconds. Stopping breathing for longer than this can create problems with visual acuity.
Also, as oxygen deprivation goes on, the body begins to cry out for air, which makes you stop paying attention to your sight alignment/sight picture and start paying attention to your need to breathe.
Depending on your shooting discipline, you can modify your use of the respiratory pause, and some air can be retained in your lungs to help establish your natural point of aim. For example, the amount of air retained in the lungs affects the vertical natural point of aim. When developing a shooting position, remember that bone support is the goal. Bones do not fatigue or stretch as muscles do.
What about when you're under physical duress, such as when hunting or in some international pistol disciplines? Then you must adapt. For example, a hunter ran a short distance, or up a small hill, to get into position to make a shot on game. The hunter stops breathing during a respiratory pause, but the crosshairs are jumping all over the place thanks to a rapidly-beating heart while the lungs demand more air. There's no time to relax to let the heartbeat appreciably slow down. What to do? Take a full breath and hold it. This will steady the position and allow for a quick shot at an animals' relatively large heart/lung area. This takes practice and should be part of any hunter's pre-season training program.
The respiratory pause is also not used to control breathing during international pistol competitions. Here the technique is to inhale as the pistol is raised from the "ready position" (muzzle pointed downward at a 45-degree angle) to the target, then the air is held in the lungs while the shot or shot string is fired. Twenty seconds is the time limit for timed fire - a very long time to hold one's breath. Shooters often train to be able to fire their complete shot string before breathing becomes an issue.
Many techniques modify the breathing cycle to support accurate shooting. The key is to experiment, have fun and discover what works best for you.