From Artemida back to the airport and then the X93 Express bus to Kifissos bus station from where the bus to Nafplio goes.
The buses Rafina -> Airport that are marked "by coast" on the timetable go through Artemida: http://ktelattikis.gr/en/en_airport_timetable
The X93 goes from the pavement between exit doors 4 & 5 of the arrivals hall. Tickets from the ticket booth next to exit door 5.
Bus to Nafplio: http://www.ktelargolida.gr/?module=default&pages_id=11&lang=en The bus to Nafplio leaves from next to the exit of the busstation. At the right of the start of the taxi queue. You will also find the ticket office for the Nafplio bus there: https://flic.kr/p/qNYqJJ
The X93 stops at the grey kiosk on the right in this picture: https://flic.kr/p/rKRUkY