I used to really dislike running up hills because I would feel so out of breath and weak at the top. If a downhill followed I recovered pretty quickly but if it was a straight away or even a gentle incline muscles would burn and I would feel really tight in the chest.
I got into studying how I move and discovered by accident that if I breathed 'strictly' from my diaphragm I didn't fatigue so bad at the top of a hill. In fact today I can reach the top of any hill and my breathing is hardly affected. Admittedly it is not only changes to breathing from my diaphragm but it sure helped a bunch!
It really served me well when I climbed Mount Whitney a couple of years ago. At aout 12,000 ft the body is looking for more air and at 14.500 ft that diaphragm better be working optimally to fill the lungs!
Check out this video to see what I discovered about breathing from the diaphragm and belly muscles.