What would be a good thesis statement describing Brutus as the tragic hero of Julius Caesar?
A thesis statement is a sentence expressing the central claim of your paper. The problem here is not that you are struggling to formulate a thesis "statement" but rather that you haven't yet developed a thesis to be stated. A thesis is a point that you are arguing. Since Brutus is widely acknowledged to be the tragic hero of Julius Caesar, it does not need to be argued; you should look for a thesis which would either need to be supported or which which illuminate some new aspect of the play for a reader.
The reason the Brutus is widely acknowledge to be the hero of the play is twofold. First, there is no one else who fits the role. Caesar dies early, Mark Antony and Octavian are the antagonists, and Cassius is a morally dubious character.
Brutus himself has the standard characteristics of the tragic hero as described in Aristotle's Poetics. He is of noble background and character, he has moral stature, and he is engaged in actions of a certain greatness or seriousness. His major flaw is that he does not realize the duplicity of others readily and is perhaps too wedded to an uncompromising ideology, not realizing that Caesar's death would fail to restore the Republic. Because of his strength of moral character, we feel fear and pity at his downfall.
A possible thesis about Brutus might be that "the way that Brutus' participation in assassination of Caesar leads to his replacement by an even more authoritarian dictator shows that an ethical system focused on desired outcomes leads to morally questionable acts with unintended consequences."
For a character to be considered a tragic hero he must possesses several qualities--he must be a person in a noble position (Brutus is a highly respected Senator from a famous Roman family); he must fall from that noble position (obviously, Brutus experiences the ultimate downfall); he must have a tragic flaw which results in his downfall (think about what personality trait Brutus possesses that leads to his death at the end of the play); and he must experience a tragic realization (this normally occurs right before the tragic hero's death; so think about Brutus realizes before he chooses to die).
Keeping those characteristics in mind for your body paragraphs, your thesis should discuss Brutus's high position and his downfall. Consider his noble goals (regarding killing Caesar) and what ultimately ends up happening to those goals.