After getting the Moon Crystal from Artemis, you are ready to find and defeat Hades.
Leave Artemis's temple and go down all the stairs until there are no more stairs. Ignore the door at the end. Jump to the left to land on the platform down there. Go all the way to the left and enter the door. You will be back outside where you encountered Dark Pegasus earlier. It's back, so either go past it or kill it, then go to the left and use the Ocarina to summon a dolphin. Ride the dolphin to the left to reach Attica.
Go to Tartarus
Go to the right from the place where you fought Lamia, until you reach the stairs. Go all the way up the stairs until there are no more stairs. Then go to the left and go through the cave door to reach Arcadia.
From the house in Arcadia, you go to the right and enter the white house if you want a password form Zeus. Then, back in the forest, go to the left until you reach the final door in the trees before the end of the forest. Follow the path, then go to the left, avoiding the spear monsters and the slimes, until you reach the small house. Go into it to reach Argolis.
Go to the far right of Argolis and enter the rightmost door. Then go to the right until you reach the second area of the cave, then go to the right and enter the second door to reach Hermes's temple if you want a password. Then leave his temple and go to the right to reach the ocean. Use the Ocarina to call a dolphin.
Go to the right until you find a small building with a door. Jump onto it and go through the door. You will be in Tartarus.
Go to the first Boss
After falling into Tartarus, use the doors Left, Left, Right, Left. If you go the wrong way, you will have to fight warriors. If you go the right way, you will end up in Cerberus's Lair.
Cerberus is a pain. The only good strategy that I have found is to stand still while Cerberus runs toward you, then jump and hit Cerberus's head directly with your sword (not with beams) when Cerberus is at the highest point of his jump. After hitting Cerberus enough times, one of its heads will disappear. At this point, you will have to hit Cerberus repeatedly in a short amount of time, because if you don't kill Cerberus, its second head will grow back.
After you have killed Cerberus, go to the far left of the room and go through the door. In this swamp, carefully go to the right, avoiding the bats, until you see a door. Go in and talk to the Nymph to get your health restored.
Back in the swamp, go to the right. There are two doors in the far right of the area. Go through the leftmost one. In this area of the swamp, kill the bat, avoid the bubble, then flip upside-down to walk along the ceiling. At the end, fall onto the branch below, then make your way to the door. Go through and talk to the old woman to get a password. If you get a game over and choose Retry after getting this password, you will restart at this location with full health.
Leave the room of the woman who gave you the password, then go to the right and flip upside-down, then go to the far right and flip the other way. Go through the far right door.
In this area made of stone, flip onto the ceiling and go to the right, carefully jumping over the pit without holding the jump button as you jump (to avoid flipping back over during the jump). Go to the right and go down where the ceiling ends. From there, carefully jump to the platform on the right (it's a long jump) and go right to reach the next area.
From there, jump to the right (another long jump) and kill the Giant Snake to the right. Then go all the way to the right, jump onto the upper ledge, and go through the upper-right door.
Go to the left and go through the door after the bridge. Then in the cave, go to the right along the upper platforms and go through the upper-right door. From there, go to the left. The door that you see along the way leads you to a Nymph who will refill your health. Continue going to the left and cross the bridge and enter the door at the end.
Go to the left and enter the door there. Then go all the way to the left and enter the door at the end. You'll be in Hades's Palace.