There is no upgrade path. The recommended way is to create a brand new Kentico 13 instance and redesign the site from scratch. This means preparing the page types, tree structure etc. and then use the Import toolkit to migrate the data. When it comes to the presentation logic and the behavior of the site and pages, you need to create the MVC code from scratch and develop the logic in the front end app.
If you want, we offer also a MVC migration service audit which can help you to decide what the next steps should be.
And here is also a video from our MVP describing what needs to be done when migrating to MVC