Ah yes, breathing. Sometimes when I give up pedalling a hill, I discover as I get off the bike that I was pretty much holding my breath. Once when I ran a relay race with gals from work I was assigned to the climbing lap (crazy assignment choice for me!). Luckily our hill lap guy from the men's team jogged back down and ran up alongside me reminding me to "Breathe OUT!, breathe OUT!, in will take care of itself!" That helped. Breathe out hard using your stomach muscles to really squeeze out the last drops (if air comes in drops), then relax and an enormous lungfull will rush in on its own.

Another thing that matters for me is not thinking about how tired I am and how easy it is to walk, but reminding myself for each pedalstroke that I'm still doing fine, still moving forward, still breathing, still rolling, still going fast enough for balance (if only barely ). Thinking about form is also a good distraction from hill pain -- back straight, neck straight, work full circles, think of a horizontal line through the circles and work each crossing of the line, relax the shoulders (releases a lot of otherwise wasted energy!), hips back (gives more power to the pedal strokes, I'm told) ... And then maybe already the next hill I'll lose all that focus, concentrate on the pain, and give up, walking the rest of the hill. But if so I tell myself I'm still moving on my own power, so it still counts. Occasionally I really need to get off and walk because my heart rate goes higher than I feel good about, but then too I keep walking. The hr goes down more slowly than if I stood still for a bit, but I don't get cold or stiff and I'm not good at starting up again on a hill anyway.