(I am not a lawyer.)
If you are writing an unauthorized biography of a celebrity, I imagine that falls under journalism and libel rules. So as long as you could cite every source you used, and you did not write anything which is demonstrably false, you would probably be okay.
You are describing what's basically an extended case study or an academic thesis. If the point of the biography is to show not this person's life from birth to some arbitrary point but to demonstrate how the artist's popularity was manipulated, strategized, packaged, and distributed, then it's really more of an industry how-to.
Your line of concern is fact and evidence. Whatever events you present as fact must have evidence to back them up: a newspaper article, an interview, a TV program, a photograph. Whatever you don't have evidence for is either conjecture (which you must label as such, and that still might not get you out of trouble) or your opinion/analysis.
A lawsuit would have grounds if you wrote something false or defamatory and proclaimed it as fact.
- Reporting on the facts of her twerking performance at the MTV Awards
is not false (as long as you describe what actually happened and can
back it up with a source). If you want to discuss and analyze why she performed that way, you
are presenting that as your opinion (which I believe is not
defamation or libel).
- If you are theorizing "she performed this provocative move to
increase brand awareness, and a poll taken the next week showed
that 27% more American adults aged 35–50 could identify her from a
photo than two weeks before the show," that's analysis based on fact. It may or may not be the reason she performed that way, but if you have the polls in question, you can make the argument.
- But if you say "she performed provocatively because she's strung out
on various recreational pharmaceuticals" or "she performed provocatively in order to piss off her conservative parents and corporate overlords," and you have no hard
evidence to back that up, that's libel, and grounds for a lawsuit.
If you're going to argue that Cyrus deliberately changed and sexualized her image in order to appeal to a new audience beyond her Hannah Montana origins, then you will have to lay out that case with a lot of facts and figures.
You can show her Q scores at different points in her career, and try to demonstrate correlation with the change in her image. You can cite polls, album sales, concert receipts, and merchandizing information. You can publish excerpts from interviews and track increases in her followers on social media.
What you can't do is speculate on Cyrus's thoughts or choices and proclaim your analysis to be truth.