Sorry to bump an old thread, but I came across this post on Google and thought I would share my experience.
I booked a trip to Ankara (from London Stansted) and received an email saying I had to check in at the airport. I booked the flight through a website called "Mytrip".
I tried checking in via the Mytrip app but that didn't work either.
I eventually got my boarding pass by going directly to the Pegasus website, entering my flight reference number, then confirming my details there.
The thing that almost caught me out is that I selected "Passport Normal" as my identity document type (the options seemed like they were badly translated to English). I had to select "British Citizen Passport" and only then was I able to proceed, eventually being able to download my boarding pass.
Hope this helps someone. Safe travels.