Where in Macbeth does it show Macbeth being his most ambitious?
This question has no definitive answer, but one can examine a few different scenes prior to King Duncan's murder that illustrate Macbeth's ambitious personality. When Macbeth listens to Ross in Act I and discovers that the witches' prophecy is correct, he immediately illustrates his ambitious nature during an aside by saying,
"If good, why do I yield to that suggestion Whose horrid image doth unfix my hair And make my seated heart knock at my ribs, Against the use of nature? Present fears Are less than horrible imaginings" (Shakespeare, 1.3.138-142).
The witches have not even mentioned murder and Macbeth is already contemplating killing King Duncan. His dream of one day becoming a king is now a possibility, and he begins to feel the urge to commit regicide. Later on in the play, Macbeth follows through with his evil intentions.
In Act I, Scene IV, Macbeth finishes speaking to King Duncan and expresses his malevolent emotions by acknowledging his ambitious nature. Macbeth says,
"Stars, hide your fires; Let not light see my black and deep desires. The eye wink at the hand, yet let that be Which the eye fears, when it is done, to see" (Shakespeare, 1.4.52-55).
Macbeth refers to his ambition as his "black and deep desires" and is now willing to commit regicide. Later on in the play, Macbeth contemplates the consequences attached to murdering King Duncan and admits that it is simply his ambition that motivates him to kill the king. Macbeth says,
"I have no spur To prick the sides of my intent, but only Vaulting ambition, which o'erleaps itself And falls on th' other" (Shakespeare, 1.7.25-28).
Macbeth's sense of ambition is perhaps at its strongest when it is first awoken in Act I, Scene III. Here, he meets with the witches and they tell him their ideas about his future. In this scene, Macbeth is so ambitious that he is already contemplating murder. It does not matter that Macbeth is internally reluctant to kill. The fact that he is mentally preparing for such an event demonstrates the full extent of his ambition:
My thought, whose murder yet is but fantastical,
Shakes so my single state of man
That function is smother'd in surmise,
and nothing is but what is not.
Similarly, in Act I, Scene IV, Macbeth also acknowledges his "deep and dark desires." This quote is also significant as it provides further proof of his naked ambition and his determination to do whatever he must to become king.
Macbeth's sense of ambition also reaches great heights in Act I, Scene VII. In this scene, Macbeth actually admits that there is no real need to kill Duncan (he has been a fair and effective monarch); he is literally only doing it to take power for himself:
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on the other.
That's hard to say. Macbeth shows a tremendous amount of ambition in Act 3, sc. 2, when he orders the murder of Banquo because he fears Banquo might suspect him of Duncan's murder. But, when he declares that he will have Macduff's family killed at the end of Act 4, sc. 1, that shows plenty of ambition on his part. Almost all of Act 5 shows an ambition Macbeth fighting to the bitter end. But the place where he probably shows the most ambition is Act 1, sc. 3 after Ross has told him that he's been named the new Thane of Cawdor, thus bringing about one of the witches' prophecies. His aside in lines 148-163 show great ambition. later in Act 1, sc. 4, when Duncan claims that Malcolm is the next in line to the throne, Macbeth's ambition leaps to the forefront again with his aside at the end of that scene.
Once his political ambition was aroused, Macbeth wanted only one thing: to become King of Scotland. Before he actually killed Duncan, however, Macbeth's ambition wavered, sometimes receding, then reasserting itself, becoming stronger each time. Macbeth's ambition reached its height with the vicious and cowardly murder of the King. Once Macbeth's ambition is realized when he is crowned, his subsequent vile acts are committed only in order to retain power.