Another native speaker. I agree with CameronAtk1, there's a difference, but also with Delstein that "She is not still tired" is odd word order.
I would say "She is no longer tired" to convey that she was tired but is not any more. I would say "She is still not tired" to mean that she has been very active and/or working very hard, but has not tired yet!
There is actually quite a large difference between the two. "She is still not tired" would be if she is not tired now, but it is expected that she will soon be tired. While 'she is not still tired' would be more along the lines of she was tired a moment ago, but she is no longer tired.
Native English speaker here. "She is not still tired" doesn't sound natural to me, and I don't think many native speakers would use that. The most natural word order to me would be "She still isn't tired." I'm not too sure about the difference in meaning, but I can't really detect one between "She is still not tired" and "She is not still tired."
I agree that "she is not still tired" is technically fine but sounds incredibly stilted, like you're making a point of negating a sentence - probably a sentence somebody else said, as a way of contradicting them.
A more natural way to negate 'still' is 'not anymore', as in 'she's not tired anymore' (or 'not tired now' if you like)