Ayane vs Subzero
Three times Ayane has tracked down and fought against Kasumi, and three times, Kasumi had fought back against her half-sister's attempts to kill her, the third time Kasumi using the Sky Torn Blast to blast Ayane to the other side of Hamarikyu Gardens.
I know Kasumi doesn't use the Sky Torn Blast. This is for dramatic purposes.
As she recovers from her wounds, Ayane hears about the Chinese ninja clan known as the Lin Kuei, and of its leader, the cryomancer Subzero. She also learns of the relic known as the Dragon Medallion, which can increase the power of its owner.
The afomentioned Medallion is also being disputed over the Mugen Tenshin and the Lin Kuei clans over its ownership. Ayane decides to head for the Lin Kuei's temple in the frozen wastelands and challenge Subzero for the medallion.