Ok so there are two ways you can do this:
A. Create a custom hook that awards users points when they becomes Premium members. In this case the badge add-on would take care of most of the awarding process for you since the badge would be awarded immediately when they receive the points. It also allows you to award badges for example users buying premium membership 6 times or more etc.
B. Hook into the Badge add-on and Paid Memberships Pro individually and connect the two via some custom code. This option would not support awarding badges for multiple payments like in option A.
The tricky thing in both options is to “detect” when a user gets the premium membership. I have never used Paid Membership Pro so I am unsure if you can do this. I will have to investigate.