In Act 5, Scene 5, Brutus is confirmed as a tragic hero. Brutus has come to the end of the battle. He knows that he is defeated. He desires to end his own life. He desires to fall on his own sword. Brutus goes down fighting. He fought until he could fight no more.
Truly, Brutus is a tragic hero. He has the qualities of a hero, and he has a tragic flaw. He is an honorable, virtuous character who is destined for a downfall, a suffering or a defeat. Brutus' fate was decided when he began listening to the wrong people. Cassius used his power to influence and persuade to get Brutus to commit to killing Caesar. Brutus loved Caesar, but he loved Rome more. When Brutus believed that Caesar had become overly ambitious, he joined the conspiracy against Caesar. This act proved to be Brutus' ultimate defeat. Even though Cassius warned Brutus to take Antony's life as well, Brutus did not want to appear as bloody butchers. This was Brutus' tragic flaw. He cared too much about what the people would think. Allowing Antony to live cost Brutus his life. Nonetheless, Brutus dies as an honorable man.
Brutus definitely endures a tragic life and death. Brutus lost so much. In fact, he lost everything. First, he had to murder his good friend Caesar. Caesar's death caused Brutus a great amount of grief. Then he loses his wife who killed herself. Cassius and Brutus are not getting along anymore. Antony is winning the battle at hand. Brutus feels the weight of everything. He can not carry on any longer.
Brutus decides that the only way out is to fall upon his own sword. No doubt, Brutus is considered a tragic hero. He was heroic in all of his deeds. Even in death, he is considered an honorable man. When Antony finds Brutus' dead body, he gives him the highest of praise:
This was the noblest Roman of them all.
All the conspirators, except him,
Did that they did out of jealousy of great Caesar;
Only he, in a general-honest thought
And common good to all, made one of them.
His life was gentle, and the elements
So mixed in him that Nature might stand up
And say to all the world, "This was a man!"
While Isumner hits all the main highlights to answer the question, I would add a few things to her analysis:
First, Brutus is in fact a tragic hero. He's a good man in heart, but is flawed by a weakness to other men's suggestion. He is a warrior and trusted advisor of Caesar, yet Cassius' influence is that of the new voice of the rising Republic. He appeals to Brutus' patriotism and persuades him to follow the movement to the point of killing Caesar; this is his deepest flaw: he doesn't follow his own loyalties and allows himself to be drawn off course.
In the normal terms, Brutus' hubris is his downfall, but his hamartia, or missing the mark, is also his problem. His noble mind leads him to take the noble pathway out of his problem, so at the end, he takes his life rather than be taken by Marcus Anthony.