I started doing a big write up on this, and I might still, but it was a pain in the hoop to figure out. If I could sniff web traffic like the Renpho app it might have been easier but this one had a lot of cookies, session tokens, verification states and redirects trying to get in through the website to scrape data.
Anyhow, a proof of concept is here, on github.
A small class allowing you to pull recent Gym activity data from PureGym.