Here's the breakdown:
* Elizabeth I was the daughter of Henry VIII and his second wife, Anne Boleyn.
* Mary I was the daughter of Henry VIII and his first wife, Catherine of Aragon.
* Mary, Queen of Scots was the daughter of Mary, Queen of Scots, who was the daughter of James V of Scotland, and Mary of Guise. Mary of Guise was the daughter of Claude, Duke of Guise, and Antoinette de Bourbon, who was the daughter of Francis of Bourbon, Count of Vendôme and Marie de Luxembourg.
The key connection is through Henry VIII:
* Elizabeth I was Henry VIII's daughter.
* Mary I was Henry VIII's daughter.
* Mary, Queen of Scots, was the great-granddaughter of Henry VIII's sister, Margaret Tudor. Margaret Tudor married James IV of Scotland, and their daughter, Mary, Queen of Scots, was the mother of Mary, Queen of Scots.
Therefore, Elizabeth I and the two Marys were all related through Henry VIII, with Mary I being Elizabeth's half-sister, and Mary, Queen of Scots, being her cousin through their shared ancestor, Margaret Tudor.