Antony is a hero of Rome. He stood up for Julius Caesar during his reign, and in Shakespeare's Julius Caesar, he avenged Caesar and Rome against Caesar's assassins Brutus and Cassius. He is a hero in the military sense; he was victorious and honorable in battle.
When Antony falls in love with Cleopatra, however, all bets are off. She still sees him as a hero, but he neglects his duties to Rome and dishonors his wife by having an affair with Cleopatra in Egypt while his wife is back home in Italy. Honor is essential to Antony's sense of self and to his identity as a hero:
If I lose my honor
I lose myself. (Antony and Cleopatra III.iv.22-3)
That's why, when he receives a letter telling him his wife has died and his fellow Roman ruler Pompey has started a rebellion, he feels he must return. But while Pompey turns out to follow a moral code similar to Antony's, and refuses to poison his enemies when he has the chance, Antony's ally Octavius Caesar renegs on the peace accord between Antony, Octavius, and Pompey, and attacks Pomepey. Because the historical Octavius would ultimately be victorius and become the celebrated first emperor of Rome, the audience might see tragedy in the demise of Antony and Pompey, who are portrayed as honorable and heroic, at the hand of Octavius, who breaks his promise and the peace.
The audience might also see Antony and Cleopatra's suicides as tragic heroic action.
Orientalism comes into play most prominently in the language used to describe Cleopatra herself, as a sort of avatar of her country and way of life. She is frequently described as being lustful and slothful, and she is clearly an influence that takes Antony from the orderly, military world of Rome to the lazy, decadent world of Egypt.