Here is a more direct solution which might work for you, depending on your actual aircraft arrival time at NAP airport:
1. Airport bus from NAP airport direct to Salerno, Piazza della Concordia
2. WALK 400 meters to the Cooperativa Sant'Andrea ferry dock near Piazza della Concordia
3. Cooperativa Sant'Andrea ferry boat to Amalfi.
http://www.sitasudtrasporti.it
http://www.sitasudtrasporti.it/public/tpl/campania/5002.pdf
(Notice that there are only FOUR airport buses per day from Monday through Saturday. A different bus company operates on Sundays. The bus fare is 7 Euros and travel time is 65 minutes.)
http://www.coopsantandrea.it
(Ferry costs 8 Euros and takes 35 minutes to Amalfi).
If the airport bus schedules don't work for you, your alternative solution is to take the airport bus to central Naples (Piazza Garibaldi, 3 Euros, 20 minutes), then the Trenitalia unreserved regionale train to Salerno (4.10 Euros, approx. 45 minutes), then walk 800 meters to the Concordia ferry dock and proceed to Amalfi on the Cooperativa Sant'Andrea ferry boat (8 Euros, 35 minutes)