One possible way of approaching this question is through two perspectives: earthly and divine. From the earthly standpoint, one could argue that Orestes acts heroically in killing Clytemnestra. After all, she was responsible for murdering Orestes's father, Agamemnon, and, according to the standards of the time, this was a serious transgression of the law which needed to be punished with the utmost severity. At this time and in this culture, law was a private family matter, and so Orestes's response was perfectly in keeping with the standards of the time. According to the dictates of contemporary law and morality, then, Orestes's actions can indeed be justified.

On the divine level, however, it's a different story. From the gods' perspective, Orestes has committed a very serious offense indeed; he is a mother-killer. At the same time, the gods are not about to strike Orestes down with a thunderbolt; they want to introduce some formal legal justice into the equation in order to take law out of the hands of families and private individuals and give it instead to a court system established for that very purpose.

Despite the best efforts of the Furies, Orestes is spared death for his crimes. More importantly, thanks to the goddess Athena's fortuitous intervention, a synthesis has been effected between earthly and divine notions of justice, one that will form the basis of the new justice system.

In this particular prompt, finding textual evident to support your findings will be critical.  I think you can use the forum here to generate thought and discussion, but you will need specific textual evidence to support and substantiate your findings. I certainly believe that Oresetes will not be able to escape the fact that he is the murder of his mother.  There will be little to dispute this fact.  The larger question might be whether he was justified in doing so.  This might be an area where you can ponder and analyze, based on what is in the text.  On the tragic hero sentiment, perhaps one can make the argument that Orestes is following the will of the Oracle in the process, and this might make him tragic.  Yet, the critical element in the tragic hero would be some particular fault or hamartia that causes their downfall.  This would have to be explored and clearly identified in the case of Orestes.