You could imagine a creature with of balloon like sacs (making up the majority of it's body) that would suck in air from the front and sequentially push air out from the bottom of its body. This would be like letting a balloon thrust air out of it (but presumably it would have some sort of fins to help it aim.)
Note: The more sacks that participate in this the less "bouncy" the flight would be (in the same way that more cylinders in a car engine causes it to run "less bumpy.")
If the creature lacked bones (using cartilage or something else lightweight) and was mostly these air sacs I think you could get this working in an earth-like atmosphere; as we have many non-animal examples of things that work this way (compressed air rockets, balloons if they are not tied, etc.) and these work without relying on lightweight gasses and don't rely on "floating."
I imagine in order sustain such a high-energy activity it may have a thin/wide maw like a whale in an insect-infested atmosphere, allowing it's travel/feeding to be the same action.
I say it would "breathe in" from the front that way Newtonian physics are still in your favor (however minor this benefit would be.)
I could also imagine a "hot air balloon" animal, again 95% of it's volume would probably be the travel method. The animal could collect burnable gasses and find some way of creating a spark to light the "spout" for the fire (if it's intelligent this is easy, if this is fully biological it would probably be some other chemicals it slurps up and combines to cause an initial burst of heat or maybe a metal that reacts with the air.)
To feed, given the awkwardness of the animal, it would probably need (again) an insect infested atmosphere and maybe a sticky film that drags the insects it runs into into the "basket" like maw at the bottom of the "Hot air balloon"-like animal.
For another temporary flight variant, I can imagine a Rocket animal; who coats it's "rocket sac" in metal that it mines, then fills itself up with gasses, then launches itself (probably for migratory reasons)
I believe each of these are possible due to using propulsion rather than floatation. They both require a light body and a large amount of energy being pushed out. While they can each be hard to believe would evolve; there are truly astounding things that have evolved on earth.
Fly larva that have virtually no brain and yet build an entire trap that filters food out of the water. Termites that build near-cathedrals. Fungus that infects ants and then bursts in order to spread itself through the colony, and the ants realizing this and sectioning off the infected members. Ants that link into bridges to handle flooding or cut leaves to grow fungus in their hive, of which they eat the fungus (and is nearly the only thing they eat.) Fish that have a light hanging off of their head just to attract fish to eat.