Currently, there is no endpoint available in Blogger API (https://developers.google.com/blogger/docs/3.0/reference/) which exposes the Popular Posts data for a blog. Google has acknowledged this and accepted it as a feature request (dating back to 2012) but till now no such public endpoint has been made available for the same.
I don't believe we expose the popular pages for a blog in any of our APIs at this point. I'll take this as a feature request =)
Refer to https://groups.google.com/d/msg/bloggerdev/G1Ew5ezZOhU/VhReyn5NXO8J