If you are building for Android you can do it 100% of on Mac OR a PC. Since Google ships sdks and tools for both Mac or PC that is why you can do this.
Apple is much trickier. You can still open iOS projects, modify code, and compile without a Mac connected. However, to actually do design in the storyboard designer in VS or build the package to deploy on a simulator or device you need to be connected to a Mac somewhere on your network. This is apple restrictions and also for the fact that all of the simulators and tooling only exists on the Mac.
You don't have to have a power house machine to do this though, something like a Mac Mini would work fine. There are some cloud solutions out there as well.
