After going through Tartarus, you arrive at Hades's Palace.
Go to Hades
Go to the right, jumping over the pits. Continue going to the right, killing the Lamia in the way (or ignoring it and going past) until you find stairs. Go up. Then jump to the left along the platforms until you find some stairs. Go up those. Then go to the right and follow the path until you are on the ledges at the top. Make your way to the right, but ignore the first set of stairs, and go up the second set of stairs. Jump onto the platform and go to the right, then go down the stairs there. From there, just follow the straightforward path until you reach an area with water. Use the Moon Crystal to reveal the shadow of Hades.
Kneel to stay safe from Hades's blows. While kneeling, swing your sword. Hades will jump away. Use this opportunity to jump and shoot a sword beam. If you are lucky, the beam will hit Hades.
Alternatively, when Hades is still swinging his sword, he will sometimes back up so that his sword won't hit you if you stand up. If this happens, try to stand and shoot a sword beam at him, then kneel again immediately. This strategy is risky, however.
Another strategy is to swing your sword at Hades's legs to make him jump away, then jump straight up and try to shoot a sword beam when you automatically crouch after you jump. Hades can't avoid these crouch-level beams, but this move is difficult to pull off.
Go to Helene
After you defeat Hades, go back to the previous room and walk up to the petrified Helene. Congratulations!