When those men confront Jen in the restaurant and she proceeds to open a can of whoop ass on all of them while describing just how awesome she is.
Jen, who's gotten a bit too smug thanks to the combination of her own natural talent and the advantage the Green Destiny sword gives her, takes on Shu Lien. The ensuing fight destroys pretty much every weapon in Shu Lien's armory — but in the end, Shu Lien wins.
A slight subversion to that lesson also doubles as an awesome entry for the sword itself. It's implied that as much skill as Jen may posses, it is only thanks to wielding the Green Destiny that she manages to hold her own against Shu Lien's absolute mastery of... pretty much every weapon ever. The sword really deserves its legendary, almost mystical status.
Li Mu Bai chases Jen in hopes that he can convince her to accept him as a Wushu master so he can pass on his skills to her. Jen says that she'll accept if Li can take her sword from her in three moves. Li does it in one.
The scene in which Li beats Jen with a random stick.
The bamboo forest climax.
Jade Fox catching and throwing back a dart shot at her by Shu Lien.