My first thought was something like a whale evolved up, but that doesn't make much sense; in the ocean, once you're big you typically keep doubling down on size.
Rather, I'd think something like a small lizard would be the base creature. It started growing larger as a defense mechanism, and storing hydrogen in sacks on its back to keep itself light. Eventually, it largely abandoned the ground, floating lazily through the air, pushing itself from branch-to-branch.
During this time, it underwent radical structural changes. It's front legs evolved into webbed, stubby wings, while it's back legs and tail elongated to reach below. The hydrogen sacks became more and more pronounced, until it no longer needed to touch the ground at all. It's tail split several times, giving it a mass of tentacles that reach down, catching onto treetops or bringing up food and water. It's mouth dropped lower than it's front legs, and grew wider, straining the bugs out of the air like a whale strains krill.
Still, it grew larger and larger. Some of its hydrogen sacks became too large to support with its circulatory system, so it stopped supporting them. Once a hydrogen sack gets old enough, it's sealed off and abandoned. It remains within the mass of the floating island, but is no longer a living part of it. The top-most layers routinely rupture, venting hydrogen into the air, and leaving a decomposing flesh bubble, which eventually turns into a kind of soil. In this soil, plants began to grow.
It's larger than a blue whale now. Small plants and animals live on top. 731
The roots of the plants reach all the way down, through the cruft on its back, and hook directly into its circulatory system. The plants get water from the creature, and in return pump oxygen directly into its blood stream. It no longer needs lungs, and develops a distributed heart network to pump blood throughout its body.
It's massive now, five, ten, twenty times the size of the largest blue whale. Much of it, however, is old-mass, not living mass. It lives high in the air, just below the tree line. It's back is covered in alpine firs, aspen groves, small mammals, birds, and insects. The plants provide all it's energy needs. It provides the plants their mineral and water needs. Its mouth has changed, looking more like a circular set of gills than a real mouth. With this, it still strains insects out of the sky.
It floats a careful line: if it stays too close to the ground, the plants on its back will grow too large and sink it out of the sky. If it floats too high, the plants will die in the cold and it will suffocate. Storms are its greatest enemy. Storms... and them... 731