Breathing while climbing is very important, indeed breathing is a cool thing to do if you want to stay alive! Breathing is something you can control to a very large extent, but only a few sportsmen, or women pay it the slightest attention. I tend to pay it a lot of attention, and it really helps me climb. I advise you to do the same.
Stephen Mifsud has held his breath for over 11 minuets! He didn't do this without training. I train in my modest way, with Five seconds breathing in, and Five seconds out, while holding yoga positions. I sometimes do 10 secs. I practise pull ups, inhaling in on the pull, and sometimes exhaling. I just play with my breath!
Have you noticed how you tense up on hard routes? Have you noticed how your breathing changes? Do you know the mechanism of breath? I have done a few activities that work on breath since I was a child, and am still relatively crap at breath control, but at least I have a couple of strategies to help me.
An expert climber should really be in control, don't you think. When we punch, or kick in the fighting arts we are told to exhale! When you do a big bunch up and dyno, your breath in, and your powerful exhale will propel you to the summit of that sequence. Do it right.
I do a bit of Yoga, a bit a fighting Art, and a bit of free diving, I am not very good at any of them, but I try. I know where my deficiencies lie. And one of them is breathing. I can feel my breath change when I am on a non standard route where the bolts are 4 meters apart. My breath is so easy to control with a bolt clipped above my head! With the same move, and the bolt 4 meters beneath my feet, it gets ragged real quick! Exercise your breath, control your breath, expel it forcibly, soften it up, and smooth it out, calm your mind, power your muscles.