Run Windows in a VM, try it under Wine, or use Microsoft's cloud version of Visual Studio. Not sure about IIS for that one though.
Better yet, stop rewarding a company that treats its users like pests and switch to open languages and servers.
Nice thought but not practical if he's developing for clients on those platforms.
If you need IIS, I doubt that you can get away without virtualisation.
The easiest path is to use something like VMWare Workstation and run Windows as a VM. You can pin Visual Studio to the sidebar, and click to run it like it was made-for-Linux app (i.e. Unity mode).
If you just need IIS (and can use MonoDevelop / Xamarin Studio) as an IDE (or just VS Code for newer stuff), then you can host IIS in a Windows Server Core in a virtual machine (less hardware requirements compared to the first option).
I just need a way to host a Visual Studio / IIS windows instance inside a Linux window manager... is that even possible?