Do not try to do too much in short time. You cannot see all of Ireland in 10 days. Spend 2 or 3 nights at each location.
Visit the local shops and pubs.
Day 1 ..Fly into Shannon. Hire Car , drive to Killarney.
Day 2 ..Visit Muckross house / Folk farm, Torc Waterfall, Ross Castle. Aghadoe for scenery.
Day 3 ..Do Ring of Kerry ...Drive own car or hire a car / driver / guide...more enjoyable, and you get to see places you will not easily find on your own
Day 4 Do Dingle & Slea Head...Drive own car or hire a car / driver / guide...more enjoyable, and you get to see places you will not easily find on your own.
Day 5 drive to Adare, Cliffs of Moher and to Galway.
Day 6 Explore Galway city
Day 7 Take day trip to Aran Islands.
Day 8 Go to Rock of Cashel, and to Kilkenny Castle
Day 9 Explore Kilkenny and area.
Day 10 return to Shannon Airport
For Day Tours see...
https://www.facebook.com/ringofkerrysightseeingtours/
https://www.tripadvisor.ie/Killarney_Tour_Taxi_Service-Killarney_County_Kerry