Hmmm. I'm not sure "bad" is a strong enough adjective for Claudius, but here goes:
Claudius is the king of Denmark, a position he attained by murdering his brother, the rightful king. To add insult to injury, Claudius also married Gertrude, the king's wife and Hamlet's mother. He is willing to do whatever it take to secure power for himself, and has no scruples about his methods.
Even though he is both Hamlet's uncle and stepfather, he also makes arrangements to have him killed. He sends Hamlet to England with Rosencrantz and Guildenstern to be executed by the English king. It is Hamlet, however, who ultimately succeeds in killing Claudius.