Poseidon's realm is the far right side of the island, past the Temple of Muses and the realm of Hades. You will meet Aphrodite and take a test on gods and goddesses. You will also acquire the Giant Pearl and the Hydra's scale.
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).
On the island
You get the offering in the Greek Mythology Museum. He has a starfish on his face, so click it and go to his palace place.
you will find pomegranetes by the creepy Sphinx thing and that is the offering.
You need to go to the statue museum, (located on Main Street) and find the Poseidon statue. It should have a starfish stuck on its face. That is the offering to Poseidon's realm. Good luck on beating Zeus, and yes, it's possible :)
in the underground cavern near Poseidon's statue
You can find the offering to Hades on Mythology Island in the graveyard. Look for a small statue or object to interact with as an offering.
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the hydra is in a underground cave near Poseidon's statue.
The offering for the Temple of Hades is pomegranates from the Garden of the Sphinx (far left). The offering for the Temple of Poseidon is the starfish that you find on the Poseidon statue in the museum.
when you go into the museum on mythology island, go right and you will come to a hall that tells you all about the gods. when you reach posiden's statue, there will be a huge pink starfish sticking to his face. this is posiden's offering.
To get Hades's offering, you go to the garden with the spinx statue. You then find a pomagranate tree and pick them. Those are the offerings.
On Mythology Island, you will meet the god Zeus, and his daughter Athena at the Tree of Immortality. You will find Aphrodite on the beach in the realm of Poseidon. The gods Poseidon and Hades are in their throne rooms, which you cannot enter until you have recovered the 5 sacred items and returned them to the Tree of Immortality.