According to Aristotle (and Shakespeare's tragedies are based on the Greek definition of tragedy), a tragic hero has specific characteristics.
First, the hero must be a great man. This does not mean that he is a great guy, but that he has achieved a reputation of greatness some how.
Macbeth is a great man: he is a valiant warrior for Duncan, the King of Scotland. His prowess in battle is recounted for the King after Macbeth defies the odds—being outnumbered—to face and kill the traitorous Macdonwald:
For brave Macbeth—well he deserves that name—
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,
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. (I.ii.18-25)
In other words, Macbeth fights his way through crowds of the enemy until he faces Macdonwald ("slave"); without discussion, Macbeth engages in life-or-death battle until he gains the advantage and slits the man open—"from his navel to his chin;" then he puts Macdonwald's head on the battlements of the Scottish castle for all to see.
The next requirement is that the hero must have a flaw that causes him to make a terrible mistake. In Macbeth's case, he is driven by "vaulting ambition:" ambition that knows no bounds.
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on the other— (I.vii.25-28)
Our hero must then die, a fate brought on by his tragic flaw. In this case, Macbeth has become a tyrant; he has murdered anyone who he even suspects of treason. Figuratively speaking, his hands are bloody with his victims (innocent or guilty) that he has arranged to have killed. He knows at one point he can never turn back—in killing King Duncan, he has lost his immortal soul. He is truly a tragic figure at the end, especially in light of the great man he once was.
In the end, knowing the witches have tricked him with their half-truths—their lies—he fights to the death. His bravery is the only aspect of Macbeth that still remains as he faces Macduff (whose family he has also slaughtered):
I will not yield,
To kiss the ground before young Malcolm's feet,
And to be baited with the rabble's curse.
Though Birnam Wood be come to Dunsinane,
And thou opposed, being of no woman born,
Yet I will try the last. Before my body
I throw my warlike shield! Lay on, Macduff,
And damn'd be him that first cries, “Hold, enough!” (V.viii.32-39)
Along with many of the heroes in Shakespeare's plays, Macbeth is a tragic hero.
in act 5, macbeth realises that he has all along been tricked and manipulated by the witches. after hearing about his wife's fact, he was demoralised and feels that life has no more meaning in it. this can be seen from the quote " tomorrow, tomorrow and tomorrow, crepts in this petty pace..." as the three prophecies come true one by one, macbeth does not immediately crumble down and commit suicide. he will not go down without a fight. as seen when he is faced with Macduff, he says that "i will not yield to kiss the ground before young malcolm's feet" doesn't this show his pride and moral honesty, traits of a hero? of course, he is still responsible for his own death as he did not accept the position god gave him. he wanted more than just being a thane. he wanted to be king and resorted to foul play to attain it. thus this led to tragic in the end where he was slained by macduff. his life is just an act, for show and he was never meant to be a king as he forced his way through. this is seen when "two happy prologues to the imperial theme of the swelling act". he tried to fit himself into a king's robes but ended up suffocating himself to death.