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NancyLebovitz comments on Expecting Short Inferential Distances - Less Wrong
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You're right - evolution might be easier than, say, how and iPhone works (not that an iPhone would work very well in Ancient Greece, or for much long, anyway). Having some high tech to show to good old Aristotle maybe would convince him you come from a very strange land, and maybe he would want to hear more of what you have to say instead of just dismissing you as a lunatic.
But imagine how much you would have to explain to make him even dimly aware of the way an iPhone works! Electronics, electricity, computation, satellites and astronomy (goodbye lunar sphere), calculus, chemistry, physics... I can barely think of all the relevant topics!
Of course, as you point out, mysoginy would be a great obstacle too. One more of the 'steps' that separate ancient peoples from modern societies.
What you want to teach depends on what you're trying to accomplish. I don't think there's much point in trying to give Aristotle an overview of modern scientific conclusions.
Assuming we want to accelerate technological progress, I'd rather teach him scientific method, decimal notation, evolution, and maybe what Feynman said (iirc) was the most important conclusion-- that matter is made of tiny bits of elements. I don't know what other specific subjects might be a good idea. Bayes? Calculus?
I don't know what would be convincing experiments for atoms.
One more I'd want to teach him that you can learn a lot by doing careful measurement and thinking about the results.
I don't know what Aristotle would come up with, given all that-- he was very smart.
Using water droplets as rudimentary microscopes.
How big a jump would it be to give them lens-making tech?
You could probably explain geometrical optics without too much trouble.