[Editors with eNotes do not write essays, but offer help to students who may need assistance.]
I hope this answer about Shakespeare's play, Macbeth, gives you some ideas of how to approach your essay by highlighting some examples of treachery in support your essay's thesis.
First of all, treachery is defined as a:
violation of faith; betrayal of trust; treason
Macbeth demonstrates a great many examples of the traits listed above throughout the play. In terms of a violation of faith or betrayal of trust, the most significant example is Macbeth's murder of Duncan. Macbeth has been a valiant and ethical soldier for Duncan, and won the King's approval and affection. When Duncan visits, there are several reasons Macbeth should not take his life (beyond the obvious argument against murder). First, Duncan is his King, and Elizabethans believed that the king or queen of the country was chosen by God, or "divine right." To kill a king (regicide) was considered a mortal sin when Shakespeare was alive. (This is also the highest form of treason Macbeth could commit.) Second, Duncan is Macbeth's friend, another basis for Duncan's trust when he visits the Macbeth's home. Third, Macbeth and Duncan are related. Duncan refers to Macbeth as "cousin." Last, Duncan is a guest in Macbeth's home, which should have guaranteed the King's safety. It was considered the worst kind of dishonor to kill someone residing under one's roof. Even an enemy was guaranteed safety by his host until he left. Duncan feels quite safe entering Macbeth's home in Act I when he says to Lady Macbeth...
Conduct me to mine host, we love him highly... (I,vi,35)
We see Macbeth's continued treachery in his murder of Banquo, his best friend—and attempted murder of Fleance (Banquo's son)—at the hands of men he convinces Banquo has wronged (which is based on lies); Macbeth also sends murderers to slaughter Macduff's wife and children while Macduff is in England visiting the legitimate ruler of Scotland, Malcolm.
Macbeth becomes treacherous and cowardly by dishonorably raising his position in the Great Chain of Being (that which dictates where someone is placed between God and the lowest creature on earth in order of importance) by killing Duncan, and anyone else he can reach who stands between him and the throne of Scotland. In killing women and children, we see that Macbeth's treachery knows no bounds.