After you get the harp from Apollo, you can rescue the Nymph and get the Sword.
Leave Apollo's temple, then go to the right and go through the first door. After that, go right and go through the first door again. Go left to the next door, then when you go to the left, you should see a tree with branches. Go leftward along the branches until you see a tall brown wall of thorns. Use the fire from the Staff of Fennel (hold Up and press the attack button) to burn the tall thorns. Then continue going to the left until you reach a dead end. Go through the door there, then go left to reach the next area.
A slime will fall from the tree, and you will see bubbles coming up from the water. Don't let the bubble hit you. Go to the left. Wait for the slime to fall, then jump over the gap as soon as a bubble has floated up and disappeared. Go to the left to reach the next area.
Go to the left and jump over another bubble like before. You will see a door in a tree. Go past it. The next bridge is where the Hydra lives. Go to the left until you see bubbles on the surface of the water. Walk to the right so that the bubbles are near the left side of the screen. From this distance, Hydra can't jump far enough to hit you, but you can hit it if it jumps far enough. Repeat the process of walking to the right so that the bubbles are near the left side of the screen, then hitting Hydra if it jumps close enough to you. If you can't see any bubbles, go to the left until you see them again.
Get the Sword from the Nymph
After you hit Hydra eight times, it dies. Go to the left and jump over the gap, then go into the door to find a Nymph. She will give you the Sword. It is stronger than the Staff of Fennel, but it can't shoot fire, so you might have to switch back to the Staff of Fennel in certain situations.
Now that you have the sword, you can get the Eye of the Graeae.