This week I'm running the pistol and rifle events for the Ohio Police and Fire Games and I've seen quite a few meltdowns.
I think the only way to get past it is to expose yourself to that stress as often as possible. The biggest stressor i saw over the last couple days was in the man on man steel shoot off. Good shooters tanked under the pressure.
Go shoot matches. Be safe. Have fun. Go slow at first. You will get better.