According to Pegasus' site, they suggest passengers to show up 2 hrs. before dept. Do you happen to know how strict are they with this? My flight is at 8:00A something so that means waking up really early to catch the bus from Taksim to the airport.
The 2 hours is just a recommendation. Their actual check-in cut-off times are 30/45 minutes:
http://www.FlyPGS.com/en/information/general-rules.aspx