Instructions
Enter the main gate of Hyrule castle in one of two ways -- you can climb the vines on a nearby wall then run over the top of the gate, or simply pay the guard 10 Rupees to let you by.
Allow a guard to catch you. When he sends you back to the entrance, you will encounter Malon from Lon Lon Ranch. Speak with her to receive a Weird Egg.
Re-enter the outer gates of the castle by climbing the vine or bribing the guard.
Follow the path until it turns left, then cut across the grassy hill on your left-hand side. This will take you directly between two guards.
Run all the way to the left-hand side of the field and climb the small wall near the castle to enter the second gate.
Jump into the moat to float by another guard, then exit where the moat turns left.
Use the Rooster that hatched from your Weird Egg to wake up the sleeping deliveryman, and then slide the milk crates to make a bridge across the moat.
Analyze each set of guards you encounter in the castle courtyard. They move according to pre-set patterns. Simply run behind hedges or around statues to stay out of their line of sight.
Navigate the courtyard in this manner until you reach Princess Zelda.