Unicycling up hill is hard work, and is probably done more for the challenge than for any practical benefits. It will always be quicker and less tiring to walk up a steep hill than to ride up.
That said, we all go for it, because you’ve got to, haven’t you. ;0)
So, here’s a few ideas:
For a very short but steep hill (such as you might find on a BMX track) ride at the hill good and fast. You may need to let the wheel run slightly ahead of you as you hit the slope, otherwise you will fall off the front of the uni. The uni should flow up the hill because of the momentum gained before you started to climb. This sort of thing is really good fun. When it works, it’s like dancing on one wheel.
On a long steady hill, just get your head down and pedal fast and smooth. Concentrate on keeping the speed up. It is possible to get up quite steep and long hills just with determination and drive.
On a steep hill, it is possible to flatten the effective gradient by turning the unicycle about 45 degrees to the slope with each pedal stroke. This means that the uni changes from 45 degrees to the right, to 45 degrees to the left (swinging through an arc of 90 degrees) in a series of short sharp movements. The path of the uni across the ground is almost straight. This technique works for the last few metres of a steep hill when you’re absolutely determined to get to the top.
Tactical hill climbing
I find this great fun. Find a landscaped area with a variety of hills, slopes, saddles, ridges and so on, and then pick a route up, angling across the steeper slopes, traverising across the very steep sections, gaining momentum on the flat sections. Eventually, you can get quite a lot of elevation, just by picking your route carefully.
Generally, you will need to stay in the seat when ‘driving’ up a hill, but as soon as you start to lose momentum, you will need to stand on the pedals. You will probably need to hold the front of the seat with one hand to stop it falling out from between your thighs.
It is possible to gain some extra power by pulling up on the seat, thus pulling your weight down onto the pedal.
Alternatively, especially with a handle, you can hold the uni steady, and sort of throw your weight up onto the top pedal and stomp it down, a bit like when you’re standing up on a bicycle.
Uphill is tiring and slow, but it can be rewarding, and it certainly impresses the public. Downhill is a lot easier.