How to build Visual Studio Solution under Linux?

I can think of two reasonable options. The first one is to create a makefile that will compile everything for you. There was once a utility called Make It So that did this automatically. Their page specifies compatibility with Visual Studio 2010, it might work with Visual Studio 2012 as well.

You can also use cmake. It's a bit more involving to get right, but the end result will be the ability to compile your code more or less anywhere.

Use xbuild? So if you install Mono, then you have xbuild which is the OSS version of msbuild. You can just build your .sln file by something like "xbuild solution.sln"