Hamlet says that comparing his father to Claudius is like comparing " Hyperion to a satyr ". Hyperion is an Ancient Greek god of light. A satyr is a creature that is half man and half goat. What does hamlets allusion suggest?

First of all, Hyperion was a titan, not a god. There is a difference. Hyperion was the titan of the heavens, the titan of light. By comparing Hyperion to his father, Hamlet was clearly communicating that he thought of his father as a benevolent and righteous king. Meanwhile, Hamlet compared his uncle Claudius to a satyr, who, as you stated, is half human and half goat. In Greek mythology, satyrs were known for being sexually promiscuous. All they cared about was women and wine. They were greedy. Hamlet is communicating that he thinks of his uncle as a greedy man who only cares about his sexual desires. The fact that a satyr is half human and half beast also tells us that Hamlet thinks of his uncle as a beastly, evil man.