Kai faces tons of archers once again. Get in the cable car and start taking the tons of archers out. Just keep at them until they are all dead.
The archers appear in different areas as you progress further along your cable car right. The trails that their arrows leave behind make the archers pretty easy to find.
The end gets rather tricky as Kai flips upside down because the cable car is falling apart. When she's upside down, up on your controller is down and down on your controller is up.
This makes aftertouching arrows to the enemies a bit more difficult. Once they are all dead and you are out of the cable car, walk down to the armory and pick up the heavenly sword.
After you pick up the heavenly sword, you will have a small cut scene and a button sequence to follow.