If you are talking about debugging a web site or api hosted in app service or service fabric, you should try using Cloud Explorer. My experiences with it have been very good.
Its pretty simple. When you open up Cloud Explorer, it shows all subscriptions and resources available to your account(s). When opening e.g. the app services for your subscription, you deployed application will be visible. You can then simply right click and say "attach debugger", as can be seen here:

You can add multiple accounts to visual studio, and select the one that has access to the resource.
This is a more extensive tutorial on how to use the Cloud Explorer:
https://learn.microsoft.com/en-us/azure/vs-azure-tools-resources-managing-with-cloud-explorer