Breathing plays an important part in maintaining your good health. Similarly, it plays an important role in how well you shoot. Holding your breath may put a temporary tamper on the in-and-out motion of breathing, but not for long. Deprived of oxygen for any length of time, the brain begins to channel your attention to its needs, not to your sight picture or trigger control.
Just as a relaxed attitude and stance are fundamental to good shooting, so too is relaxed breathing. Keep the oxygen coming until the very moment when the shot is fired. Gentle rhythmic breathing to that point is desirable. As you are exhaling, stop midway, gain your sight picture, squeeze off the shot, and resume breathing.