There are many ways in which Frankenstein's monster can be tied to being a tragic hero (as defined by the text in Mary Shelley's novel Frankenstein).
According to Aristotle, a tragic hero possessed certain characteristics, qualities, or faced certain circumstances.
These characteristics, or circumstances, will be defined, paired with how the monster coincides with them.
1. Though the tragic hero is pre-eminently great, he/she is not perfect.
While not "great" under the original sense of the meaning (in regards to Aristotle), the monster was created by Victor to be "contrary to my first intention, to make the being of a gigantic stature." Therefore, Victor's initial concern, and intent, was to make the monster "pre-eminently great."
2. The hero's downfall, therefore, is partially her/his own fault, the result of free choice, not of accident or villainy or some overriding, malignant fate.
The given that the "hero's downfall is only partially his/her fault, the monster can be paralleled to a tragic hero based upon the fact that if Victor would not have abandoned him, the monster would not have begun his murderous rampage. Therefore, while the monster is partially responsible, he cannot be found completely responsible for his fault.
3. The fall is not pure loss. There is some increase in awareness, some gain in self-knowledge, some discovery on the part of the tragic hero.
By the end of the novel, the monster comes to acknowledge Victor's true place in his life. The monster's need to be accepted, and forgiven, coincides with Victor's death. The monster, enlightened by the trials and tribulations he has faced, comes to be a sympathetic being.
4. Though it arouses solemn emotion, tragedy does not leave its audience in a state of depression.
Mary Shelley's novel can leave readers with two different feelings. One feeling coincides with Victor's death. The entire reason Victor dies in the end is because he brought the monster to life. Some may feel his death is tragic, without feeling depressed given he deserves this fate (he created the monster).
Another reason readers may not feel depressed at the end of the novel is because the monster dies. Some readers may feel as though the monster deserves his death given all of the lives he took.