He's Da Man and one of the most universal creative forces that there ever were. There is a reason Shout-Out to Shakespeare is such a large trope and that his plays, characters and quotes are Trope Namers.
Some works of fiction would have you believe that he's the only dramatist who wrote plays and did theatre. His plays are the only ones ever written — and then only a few of them ever show up. They're usually the tragedies, such as Romeo and Juliet and Hamlet.
There have been only two circus companies ever: Ringling Bros. and Barnum & Bailey Circus (traditional) and Cirque du Soleil (contemporary). And don't expect depictions of the latter to acknowledge that it presents a variety of different productions and draws on an international talent pool — it's almost invariably presented as a single troupe that only employs French/French-Canadian performers. If you're from the Greater Los Angeles (California) area, you can add Circus Vargas to the above list, and New Yorkers can add the Big Apple Circus.
Only lion tamers ever? Clyde Beatty (the guy who invented using a whip and a chair) or Gunther Gabel-Williams.
Aerialists? The Flying Wallendas (or maybe the Zacchinis, if you're at least a casual circus buff).
Clowns? Pretty much just Emmett Kelly. (Bozo, Clarabelle, etc. don't count because they weren't actually circus clowns.)
Sideshow performers? General Tom Thumb or Chang and Eng (the "Siamese twins").
Famous circus animals? Just Jumbo the Elephant (and when it comes to fictional circus animals, Mrs. Jumbo and Dumbo). Old Joe the Dromedary is only known indirectly, as the model for the camel on the Camel Cigarettes pack...and eventually for the most controversial advertising mascot in history, Joe Camel.
Magicians? Harry Houdini (never mind that he was an escape artist, not a magician). Maybe David Copperfield and Siegfried and Roy if you're lucky.
There are only three French playwrights : Corneille, Racine and Molière - who all lived in the same century. Also, Corneille only ever wrote Le Cid ; never mind that it is fairly atypical compared to the rest of his work.
Shakespeare both embodies and defies this trope - he put in a lot of references to very famous (in his time) figures, but also dug up some obscure things. He designed his plays to appeal both to the intellectuals and 'the groundlings'.