Zhang Ziyi aka Ziyi Zhang

Equally-adept at comedy, drama, and action, Zhang Ziyi (or Ziyi Zhang, depending on the translation) isn't a martial arts expert, but, like fellow Fantastic Femme Michelle Yeoh (with whom she's co-starred twice), she uses extensive dance training to learn the needed choreography!
Next up, she'll be playing a live-action version of the legendary Chinese heroine Hua Mulan!
Trivia:
Didn't know any English when she did Rush Hour 2! She learned her dialogue phonetically and star Jackie Chan translated the director's instructions for her! (She has since learned English.)

Genre appearances include...
Mulan [2011] (Hua Mulan)
Sophie's Revenge (Sophie)
HorseMen (Kristen)
TMNT (Karai)
House of Flying Daggers (Mei)
Hero (Moon)
Warrior aka Musa (Princess Bu-yong)
Purple Butterfly ( Cynthia / Ding Hui)
Legend of Zu aka Zu Warriors [2001] (Joy)
Rush Hour 2 (Hu Li)
Crouching Tiger, Hidden Dragon (Jen Yu / Xia Long / Jiao Long)

Check out...
Her Official Site
Hello Ziyi (FanSite)

Other actresses to play Karai include...

Karen Neill in Teenage Mutant Ninja Turtles [2003]
Other actresses to play Hua Mulan include...
Wei Zaho in Hua Mulan [2009]
Ming-Na and Lea Salonga (singing) in Mulan [1998] / Mulan II / World of Mulan [2005]
Anita Yuen in Mulan [TV][1998]