The main elements in the Medusa story include Medusa's initial beauty which was so drastically changed. Her new form with the snake - haired head and the petrifying gaze. Then there's the backstory of why she was cursed, involving the actions of Poseidon and Athena. Perseus' journey to defeat her is also key. He had to be clever and get help from the gods. For example, he got a sword from Hermes and a shield from Athena. After her death, the power of her head remained, which was used in various ways in other parts of Greek mythology.
One important element is the curse put on Medusa by Athena. This curse changed her appearance completely. Another is the role of Poseidon in the story, as his actions in the temple led to Medusa's downfall. And of course, Perseus' adventure to slay Medusa, including how he obtained the necessary items like the winged shoes and the mirrored shield, is a crucial part.
The main elements are Medusa's transformation from a beautiful woman to a Gorgon. Also, Perseus' quest to kill her and the use of her head as a weapon.