The rising action is when Brutus and Cassius are fleeing for their lives. Trying to prevent tyranny, Brutus is now escaping the tyrany of Caesar's ghost.
With the assassination of Caesar, all of Rome is plunged into a civil war. The action rises as Antony's and Octavian's forces fight Cassius' and Brutus' forces.
Antony's forces defeat Cassius' forces and Cassius kills himself.
Brutus rallies Cassius' men and they fight until Brutus realizes it is hopeless. The climax occurs when Brutus falls on his own sword, thus dying an honorable death.