For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Orestes arrives in Argos, meets his sister and mother, and discusses the situation with Zeus. The act ends when he commits to staying in town.
Act II
Electra tries to save the people of Argos – to no avail. Orestes experiences his epiphany and resolves to kill the royal couple. He does so. The act ends when he and his sister head for Apollo's shrine.
Act III
Electra and Orestes deal with the furies in the aftermath of the murders. Orestes verbally dukes it out with the king of gods and wins, though he loses Electra in the process. He delivers his "coronation" speech and leaves town.