Macbeth was brave in Act I. In Scene 2, the bloody soldier describes how Macbth bravely fought for Duncan.
For brave Macbeth—well he deserves that name—
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,(20)
Like valor's minion carved out his passage
Till he faced the slave,
Which ne'er shook hands, nor bade farewell to him,
Till he unseam'd him from the nave to the chaps,
And fix'd his head upon our battlements.(25) (Act 1, Scene 2)
Macbeth clearly acted not out of ambition, and did not care about himself. He killed the traitor, the Thane of Cawdor. He is rewarded with the title.
Macbeth unfortunately goes downhill from there. He does demonstrate bravery of a sort in asking Duncan to his castle. He stands up to his wife, briefly, when he decides not to kill Duncan. His bravery does not last.
Finally, Macbeth is brave when he kills Duncan. The bloody dagger seems to have given him the strength to do it (as well as Lady Macbeth’s prodding).
Is this a dagger which I see before me,
The handle toward my hand? Come, let me clutch thee.
I have thee not, and yet I see thee still. (Act 2, Scene 1)
Lady Macbeth feared that Macbeth was too full of “the milk of human kindness” but he did the deed.
From here it is a little unclear what constitutes bravery or crazed cowardice. Macbeth does not act brave when he hires murderers to kill Banquo instead of doing it himself. He also certainly is not brave when he sees Banquo’s ghost. However, instead of giving up and fleeing he stays and carves a bloody path, as he did in battle, to keep his throne.