Thinking just slightly outside the standard theatrical box, I'd submit Salome of the Strauss opera. She's onstage for almost the entire work, has to sing one of the most difficult roles in contemporary opera, has to act, *and* has to convincingly handle the Dance of the Seven Veils.
And if you've ever seen a *bad* production (like, oh, I dunno, maybe the new one at the Met), you know what a mine field that role can be.
"That duck was a sexual toy, and it was on display!" -- an unknown Nashville town leader