The Pephka Islands is the Eastern half the south eastern most island.
Obsidian Islands are Hyrda and Melos, located east of Lakonia on the main continent.
Abantis are Euboea and Skyros located just south of Makedonia (triple peninsula).
The achievement is for 20 combined quests between the 3 locations. There are plenty of quests available between the 3 locations. Pephka has 2 different quest lines for Minotaur that have 4-6 quests to complete. Also the smaller quests (black diamonds) count as well.
It is confirmed that you don't need 1 per island, just 20 total between the areas
Solution sourced from DeliriousDrew:
https://www.trueachievements.com/gamer/DeliriousDrew