General:
* Actress
* Entertainer
* Artist
* Songstress
* Vocalist
* Dancer
* Musician
* Showgirl
* Performer
* Talent
More specific:
* For singing: Soprano, mezzo-soprano, contralto, singer
* For acting: Thespian, player, dramatic artist, stage actress
* For dancing: Ballerina, dancer, choreographer
* For comedy: Comedienne, humorist
You could also use a more descriptive phrase like "a woman who performs" or "a female artist." The best synonym will depend on the specific context and the type of performance you're talking about.