You need to try to maintain your cadence. Shifting gears is how you do that. Try buying a cheap cyclecomputer with cadence and experimenting with it. When you hit a hill, unless it is a really short one, you should gear down until you can keep up the same cadence you would on flat ground. It looks like your bike has an 8-speed hub, so you should have an easy time shifting, because you don't have a front derailer to shift.

Or, you could experiment with standing when you climb. It works better for some people.

Personally, when I am on a short hill, or an overpass, I just power through it standing up, it is easier and faster than staying seated and gearing down. But for longer hills, I have to gear down otherwise I get tired really quickly.