As we've pointed out elsewhere in this guide (see, for example, our "Booker's Seven Basic Plots Analysis" of the play), Aeschylus's Agamemnon is a very atypical tragedy. This is because the tragic hero is offstage most of the time, and doesn't really do anything other than show up and get killed.
Still, we do learn enough about Agamemnon from flashbacks narrated by the Chorus that it still makes some sense to think about him in this role. Agamemnon's single most important action, which we hear about but don't see, is his decision to sacrifice his daughter Iphigenia. It is this action, after all, which enrages his wife Clytemnestra, and inspires her to kill him in revenge. In this way, we can say that Agamemnon is the protagonist, and thus responsible for his own fate. Of course, as you'll see if you turn back to the Chorus's first song, it's very unclear how much choice Agamemnon had in the matter, and we don't ever actually learn how the sacrifice played out. Oddly enough, Agamemnon's main action is shrouded in mystery, another feature that makes him a very unusual protagonist.