Do a few balance-training exercises every day. Examples: walking (forward and backward) heel-to-toe along a straight line, or standing on one foot with your eyes closed for 20 seconds. Or throw in balance elements during a hike: Scramble over some rocks, walk (or run) the length of a log, slalom through the trees. Not only will you improve your sense of balance; you’ll also increase your heart rate.
Be persistent about push-ups and/or pull-ups. If you need to self-arrest on the mountain, or help another climber, upper-body strength is vital for both endeavors.
Add intervals to your climbs or runs. Pick up the pace for 30 seconds to 2 minutes (mix it up as you go), then slow down and go again; repeat up to 10 times. Intervals are a proven way of increasing cardiovascular capacity; the greater your capacity, the easier it is to deliver that coveted oxygen at 14,000 feet