A.C. Bradley, the great Shakespearean critic, describes Cleopatra in Oxford Lectures on Poetry as a non-dramatic and non-tragic character. This is a bit of an oxymoron as it is applied to one of the protagonists in a dramatic Shakespearean tragedy. Bradley states that in Antony and Cleopatra, Shakespeare could have done much more to create dramatic tension and the revelation of turbulent inner emotion.
For instance, Bradley holds that in the first parts of the play, Cleopatra is shown in non-emotive ways, ways that we might term character background. He contrasts the first three acts of Antony and Cleopatra with Romeo and Juliet, the latter of which is loaded with violent emotion and violent action. But the former shows Cleopatra with her ladies in waiting; alternately beguiling and tormenting Antony; asking questions about Octavia's personal appearance.
Cleopatra's most active scene is when she threatens the messenger, which is a scene, Bradley contends, that is completely dispensable as it has nothing to do with the plot. Additionally, Bradley asserts that Cleopatra's scenes do not "bode" tragedy. She is shown as "irresistible" but she is not shown as having powerful inner emotions that enhance the tragic qualities and motivate the plot.