I think the "bloody tyrant" part is pretty self-evident, so let's think about the "tragic hero" part. Aristotle sets out the key elements of tragedy, and they include the following:
1. A character must fall from a high place. It seems to me that Macbeth's true fall was not from his position as king but from his position as trusted cousin and soldier of the King to a murderous tyrant. From that position he falls; he is king, but he's not respected or revered so his fall goes nearly unnoticed or worse--it's seen as a relief.
2. The character must fall, in large part, due to his own behaviors. That's certainly true for Macbeth.
3. The character must receive a punishment which is generally more than he deserves. Most of us, I think, would say Macbeth deserved every bit of what he got--and perhaps more.
4. The audience must feel pity and fear (awe). There is certainly some sense of awe or fear for the audience when it considers the situation of Macbeth; however, we feel little sympathy for him until maybe his wife dies. It is then we sense his despair and hopelessness. The audience is quick to say he brought it all on himself, of course; but we do have a sense of pity because of his final self-awareness and resignation.
In short, Macbeth is probably as much tragic hero as he is bloody tyrant, making him one of the most tortured and tyrannical protagonists in Shakespeare's works.
macbeth turned to be a bloody person who became convinced that shedding blood was the only way to achieve his ambitions he started his massacres by killing the king in order to take his position then he killed banquo in order to let his chilldren be kings and not banquos what was even more brutal was the fact of killing macduffs wife and children an action an action which showed how bloody and hard hearted this person became however at the sametime this last massacre especially was the straw that broke the camels back it set people against him and many of lords joined malcoms army against macbeth
macduf was a member in this army and he was the one who killed macbeth at the end this macbeth was the one who was after all the crimes involved in the play except the last bloody deed as he was the one being murdered