The concept of a "tragic hero" is specific to an aristocratic cultural milieu, and functions to locate the hero as almost an intermediary between the divine and the human. Most ancient tragic heroes trace their lineage back to the gods and are thus themselves demi-gods. Even in Renaissance tragedy, the protagonists we consider tragic heroes are usually kings or nobles. What makes this significant is that it means that they are not just private individuals, but rather emblems of the state (as in Louis XIV's famous dictum: "L'État, c'est moi.")
Mary Shelley's novel Frankenstein is not a tragedy at all, but rather, as most novels, an exemplar of modern bourgeois society. Victor, while wealthy and intelligent, is not a king or a demigod, merely an amateur scientist. While he is a deeply flawed protagonist, he is not an actual Prometheus, because a modern scientific mentality is not compatible with notions of humanity as consisting of a hierarchy ranging from kings who are close to gods in their nature and peasants who are almost animalistic in nature. Literary genres are always part of their specific cultural circumstances and beliefs. In fact, we can see Shelley's novel as about both the inadvisability and genuine impossibility of there being a real modern Prometheus, and in Victor's failings, we see a condemnation of the pretensions of mortals to such powers.
Mary Shelley's protagonist, in her Romantic novel Frankenstein, can be identified as a tragic hero if aligned to some of the characteristics of the traditional tragic hero.
The tragic hero, as defined by Aristotle in Poetics, must be noble in stature and possess greatness, is mortal and imperfect (although deemed great by society), possesses harmatia (which is Latin for a tragic flaw), is not completely at fault for their misfortune, discovers something from his/her fall (therefore, not a total loss), and his/her end (demise) does not leave the audience in a depressed or completely saddened state.
Based upon these characteristics, Victor can be aligned with a few. Victor's family is renowned in Geneva (which aligns with noble stature). Victor is also a mortal (completely human with no allusions made to anything different). His hamartia is his obsession with science and reanimating life. His fall is not completely his fault given the early education in science his father helped to flourish. In the end, he finds that he should not have pushed God in his quest for Forbidden Knowledge.