I have Oracle SQL Developer already installed and am able to connect to and query Oracle databases.
Using Help -> Check for Updates I was able to install the Oracle MySQ
You may find the following relevant as well:
Oracle SQL Developer connection to Microsoft SQL Server
In my case I had to place the ntlmauth.dll
in the sql-developer application directory itself (i.e. sql-developer\jdk\jre\bin). Why this location over the system jre/bin I have no idea. But it worked.