How do you get to Poseidon on Mythology Island?

You can enter the realm of Poseidon from his temple at the far right of the island. Use the starfish (from Poseidon's statue in the museum) as an offering on the altar.

To get to the throne room (except as a glitch), you will need Hercules. Hercules will not help you until you have returned all of the 5 sacred items to the Tree of Immortality. Get the Touchscreen Mirror from Aphrodite on Poseidon's beach, so that you can transport Hercules to the realms of Poseidon and Hades (he does not like to walk).