Get the Pomegranates from Herc's Hero Hut! Then, offer them at the offering alter which is located in Hades' temple in the grove of temples. Then, play the song you learned on the pipe that you should have retrieved from Apollo's Temple(the music temple) that is located on the hill on the left of the Underworld. Cerberus will fall asleep and you simply must grab a whisker.
To retrieve the Hydra Scale:
Go to the Museum and retrieve the starfish attached to the face of a statue. Bring it to the Temple of Poseidon located on the hill on the right of the underworld. Offer it as a gift. Enter the Water Temple. Play the god-guess-game that Aphrodite gives and when you get all the answers right, you will recieve a tele-mirror that you can use to tele anywhere. Swim into the underwater cave. Jump on the hydra's heads when it strikes and when it's completely unconscious, take a scale.
To retrieve the flower:
Pull all the levers and release the 2 wooden pipes until all the water flows. Then, go back to the goddess and she'll give you the rainbow rose.
The Pearl:
Get the pearl when the clam is open near the underwater cave.
I don't know about the ring, I will tell you when I get it!