In FFXIV, Island Jellyfish is a type of crafting material acquired on a player’s Island Sanctuary. It can be found inside of Coral Formation gathering nodes underwater. These appear on the far eastern side of the map in the submerged section of the Coral Sands area.
Note that you must first craft an Islekeep’s Bronze Gig. Attempting to gather from a Coral Formation before that point will only yield Island Coral. After the gig is crafted, every gathering attempt will yield both one piece of coral and a single jellyfish.