You only need steps 1, 3 and 4 (you can do step 2 if you want Python, but it is not needed).
Don't skip the pacman steps! I also added autoconf, bash, flex, wget, vim, sed, tar to the list of packages I installed with pacman. You'll need some of these to get Nemo to install. Some are just useful.
If you install the 64 bit version of Julia (Windows 64) you will need to install mingw64 with the x86_64 version (not i686). Otherwise you will want mingw32.
3) Make sure msys2/mingw m4, sh, make, gcc etc are in your Windows PATH (Control Panel, system, advanced setting, environment variable).
On my system the relevant path was C:\msys64\mingw64\bin but it depends where you install everything, obviously.
Before Nemo will actually work, you will need to add it to your PATH. On my machine the path was C:\Users\user\.julia\v0.3\Nemo\src\lib This should be the same for you with "user" replaced by your username. The path won't actually exist until you do Pkg.clone(...) from within Julia.
If you cannot get Nemo to work on your machine, it is unlikely we can help at this stage. We plan to release a binary version for Windows in the future which will be better supported and 100% easier to install.
DLL's are a nightmare and old versions of mingw could be hiding anywhere.