The Easy Way

Hint 1 of 7:

Sometimes you will have to try the next step a few times until the drawbridge
is down.

Hint 2 of 7:

From the alligator screen go to the left.

Hint 3 of 7:

If the drawbridge is down, there should also be a guard with a cart waiting
for something.  If not, go off screen and come back.

Hint 4 of 7:

He's waiting just long enough for you to DO something.

Hint 5 of 7:

Walk up to the cart and jump in.

Hint 6 of 7:

Once inside, jump out.  Voila!  You are now inside.

Hint 7 of 7:

If you don't jump in but follow him instead, you will get caught and thrown
into the dungeon.