That particular hill
That particular hill (truckers call it the "Vegas overheater") will make almost any small engine struggle. Don't expect the c to fly up it like a Camaro with its 350hp, but it won't struggle like a '74 air cooled VW Bug either.
I'd expect that if it's not weighed down, the Prius c would do just fine on that hill. I've pulled that hill multiple times in various vehicles and all but the largest of engines will have to work on that grade. Parley's Canyon in Utah (Salt Lake City to Park City, I-80), Snowqualmie (Seattle, I-90), and the Grapevine (LA to Bakersfield, I-5) are all hills most cars will struggle with.
Besides, no matter what car you're in, you can always look at the poor truckers in the right lane as you pass them by. :)