It depends on your evolutionary path
The trick with evolution is there is no grand goal - there are incremental advances that at the time make sense, either sexually or on a survival basis.
So to consider what atmosphere would be required to meet your criteria the answer is really that it depends on the incremental evolutionary path up to that point.
I would imagine, for instance, that our current-day floating spiders (called ballooning) are good examples, where traditionally land-based creatures used techniques already at their disposal to eventually fly, and this then became evolutionarily locked in.
Your creatures would evolve similarly: there would need to be a pathway up to the point where they are already inflating, already can control to a degree their direction, and already around about the same size, for them to then make a 'small' leap to be then a large floating organism.
As far as the atmosphere goes, there are several characteristics I would imagine it could have for this 'small leap' to be evolutionarily advantageous:
- it should be desirable for your floating organism to be in. This means either it provides them with a mating advantage (they can float far away to spread the genetics further), or a survival advantage (they can evade land based predators)
- it should be relatively easy for your organism to be in. So no huge wind factors that would make it hard for your organism to make this leap. I guess a denser atmosphere also helps, as less inflation is needed to accomplish the same goal.
- it should be safe for them - ie. they won't die straight away if they do this. An absence of predators up there would help. Atmosphere could also be 'cloudy' so vision based predators have a difficult time finding them.
- it should be 'sexy' for them. If sexual reproduction is available on your world, which I believe it needs to be in order for the diversity of life to get up to the requirements you have outlined, then there needs to be competition and sexual selection. This means a female should really be 'awed' by the fact the male can do this, or the other way around, to promote competition within the same species and push these evolutionary developments. Perhaps the atmosphere can carry sound easily for mating rituals, or your organisms can carry scent to advertise their sexy presence (meaning not too much wind again).
Again there is no goal in evolution, there is no real reason why it hasn't happened on Earth, other than perhaps it isn't really sexy enough yet for our organisms that can 'almost' do this.