On Shadow Island you can start the Shadow's Mark quest which requires you to complete the indicated challenge. On this page you'll learn what you must do to obtain the Island Soul.
Shadow Island is located north of Vern. You can get an Island Soul by completing all the location's quests. One of these can prove particularly troublesome: Shadow's Mark. It tasks you with completing the Shadespire's 24th floor. This quest proves problematic for those who haven't tried the Tower challenge yet. Shadespire is the first area of the Tower activity available in cities.
After starting the quest head to a big city such as Vern Circle and find the Tower. After you interact with it you can brave the challenges it holds. Before you can get to the 24th floor you must have enough ilvl, in this case 420 ilvl. After completing the 24th floor you can return to the island, complete the quest and obtain the Island Soul.