A floating island is a mass of floating aquatic plants, mud, and peat ranging in thickness from several centimeters to a few meters. Floating islands are found in many parts of the world. They exist less commonly as an artificial phenomenon.

Sometimes referred to as tussocks, floatons, or suds, natural floating islands are composed of vegetation growing on a buoyant mat of plant roots or other organic detritus.

Without unobtainium, or zonai magic, that's not really possible. It's a nice idea for science fiction, but the laws of physics apply universally & sky islands still need to obey the laws of gravity & thus would not exist.

But floating islands do indeed exist on six of the seven continents and sometimes in the oceans between them. These islands are kept buoyant by the light spongy tissues of certain aquatic plants, by gases released into their soil by decomposing vegetation, or by both these forces.