Here is 1 really simple breathing technique that can be used by just about anyone during that really strenuous ascent or during high altitude treks or when you run out of steam when you are attempting the staircase of a 10 storey building.
The trick is simple. Hyperventilate. And do this with your mouth closed. A controlled rhythmic conscious hyperventilation increases the oxygen in your blood. At high altitudes, your body automatically increases your breathing rate for acclimatization. However, doing it yourself aids the process. As you ascend, oxygen levels in the atmosphere drop necessitating compensation by breathing deeper or increasing breathing rate. Here is a chart that shows the drop in pressure and oxygen with increase in altitude.
Please don’t hyperventilate at sea-level as this leads to an increase in blood pH (making it more alkaline)(alkosis) due to reduced CO2 in the blood.
Hope this helps when you get sucker-punched during your next high-altitude ascent!
p.S: I am not a doctor.