How was Macbeth a bad king or a tyrant? What is the criteria for being a good king?
I think that this is a very hard question to answer. I think that many kings, fictional or not, possess both the bad and good traits of being a king.
In regards to Macbeth, he certainly possessed the ambition many would wish for a king. He was brave, as noted by Duncan and the title of the Thane of Cawdor. He was protective, as noted by his murder of Banquo. Macbeth was even proud, as seen by his desire to keep the new title of Thane before taking the crown.
Unfortunately, many of the characteristics one would align with being a good king made Macbeth a bad king as well. Macbeth was too ambitious--as seen by his murdering Duncan. He was too protective--as seen by his inability to interpret the apparitions warnings in the correct way. Lastly, he was too proud--as seen by his refusal to leave the castle as Birnam Wood "moved" against him.
Like anything, one must always have control. Too much of anything normally turns out to be a bad thing. Therefore, depending upon one's individual views, Macbeth could be both a bad king or a good one.
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In Act 4 scene 3 Malcom refers to Macbeth as being a tyrant “This Tyrant, whose sole name blisters our tongues”.(4.3.12) Macbeth doesn’t trust anyone. He deceives and manipulates others so he can become king. Macbeth has too many enemies to keep track of, he draws more attention to himself with every murder and he can’t live with his conscious. Ultimately, Macbeth proves himself better suited to the battlefield than to political intrigue, because he lacks the skills necessary to rule without being a tyrant. His response to every problem is violence and murder.