Alright... A female Chinese circus acrobat in the Old West.
First, it'd have to be something obviously noticable from a distance.
Second, a 'traditional' Chinese circus costume for the era would most likely cover all but the hands and head (especially for a woman).
Visually, that leaves you with the hair, the face, the hands and the costume itself.
Hair is easy... At the time, most all Chinese wore their hair very long. Perhaps hers was cut very short (to disguise her aas a boy perhaps?). Color would be another easy one, since black is by and large the most dominant hair color amongst Chinese. A distinctive hairdo might also work.
Face is a little bit trickier, unless you can get a very close look... Eye color is too subtle from a distance; the eye would have to be completely missing (an eye patch, due to an accident with a juggler maybe? loss of depth percetion would make her acrobatics all the more notable). The missing tooth isn't a bad idea, although a gold/silver/other tooth might work just as well. I'd avoid tattoos, myself... They're a little cliched, and quite over-used.
Costume is another easy one... Every circus acrbatic troupe is going to have it's own distinctive outfit. It doesn't even need to be the whole costume. A hat, scarf, shawl, bandanna, jacket or robe of a particular style, cut or color would work.
Also... Does the other player need to recognize you from a performance? What about advertising posters for the circus?
Presenting
THE AMAZING CHOWS!
Masters of Acrobatics, the High Wire, and the Flying Trapeze
Or some such.