Instructions
Run into the first room and approach the guard with Link. Speak with the guard so he diverts his attention away from the path, and then hit the Switch button to take control of Zelda.
Run behind the guard as Zelda to the room's exit. Switch back to Link and run out the door.
Avoid patrolling guards by running behind them or out of their field of view. You can get by most while controlling Link, with Zelda automatically running behind.
Speak with stationary guards to turn their attention and keep switching back to Zelda to run past. This will get you all the way through to the last guard.
Pick up the large rocks near the last guard. He will not turn to talk to you, so you will have to make a ruckus instead. Throw the rocks to get the guard's attention, then switch to Zelda and make a break for it.