Turn away from Medusa's eyes to avoid her petrifying gaze. In Castlevania: Belmont's Curse, the Guardian's Gaze clue in the Underground Ruins gives you the warning before Medusa: looking at the eyes leaves you unable to move. You also cannot grapple onto Medusa herself.
How do you avoid Medusa's Guardian's Gaze?
Turn away from Medusa when she uses her gaze so you do not become immobilized.
The Guardian's Gaze clue comes from the spirit beside the candles in the Underground Ruins. The spirit saw the monster's eyes, could not move or hide, and should have turned away.
When Medusa calls for you to look into her eyes, turn Rose away. Don't stay facing her for one more hit: getting frozen in place costs you far more. For the other encounters, follow the Castlevania: Belmont's Curse bosses page.
Can you grapple onto Medusa?
No. Medusa can't be grabbed with the whip, so use the anchors around the arena to move instead.
What do you get after beating Medusa?
Defeating Medusa gives you The Prophetess card with Petrifying Gaze, which petrifies enemies in front of Rose.
On the reward screen, hold to equip the card or choose Continue. The effect applies to enemies in front of Rose, so face the enemies you want to petrify when using it. See the Castlevania: Belmont's Curse tarot cards page for the card system.
Medusa is sealed into the card and you get the last key. Take it back to the Gate to the Catacombs; the walkthrough has the full route.