A good way to start is by offering Aristotle's definition of tragedy. In his Poetics, he says:
“Tragedy, then, is an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; with incidents arousing pity and fear, wherewith to accomplish its katharsis of such emotions..."
Based on this definition, we can say that Agamemnon's actions are serious. He sacrificed his daughter to Artemis to get favorable winds, he fought a long war at Troy, and he now has to face his wife, Klytemnestra, who hates him.
To be sure, Agamemnon is a person who can be despised for the sacrifice of his daughter, but in a culture of war this action is almost understandable. After a long war, he comes back home instead of a reception, he is killed in cold blood in a bath by his wife. There is some pity here.
Finally, there is a sense of fear and katharsis as well by the final scene. The tension is resolved by the death of Agamemnon. No one is left wondering what will happen.
The concept of a tragic hero derives from Aristotle, who developed the notion as a way of describing what made a good protagonist in a Greek tragedy. He argues that the tragic hero should be a character who is greater and more noble than most people, involved in actions of a certain seriousness, and whose downfall evokes fear and pity in the audience. The character in question cannot be a completely evil one, for we do not feel pity at the downfall of a villain, but instead someone admirable but flawed or someone who makes a bad decision at some point.
The main problem with the question is that the protagonist of Aeschylus' Agamemnon is not Agamemnon himself but his wife Clytemnestra. She is the one who dominates the play and undergoes a moment of crisis when her husband, the murderer of her daughter, returns home from Troy. In this play, Agamemnon is a fairly static character, the object of Clytemnestra's decision rather than the one making the fateful decision. Thus although a play could be written in which Agamemnon was portrayed as a tragic hero, he is not actually the protagonist of the Agamemnon.