I found the solution after poking around in the /usr directory for awhile. I advise anyone else struggling with this problem to do the same to familiarize themselves with mingw-w64.
the pkg-config command for mingw-w64 on arch is:
i686-w64-mingw32-pkg-config gtkmm-3.0 --cflags --libs
However, in order to use the above command, one first needs to install the following package on arch: mingw-w64-pkg-config (from the repo linked in the question)