In "Last Action Hero"
In the film, Vivaldi was the main villain of the Jack Slater movie "Jack Slater IV" and the secondary antagonist of film.
He was the richest and most powerful Sicilian mafia boss in LA. His henchman Mr. Benedict (the main antagonist of the movie) hates him and kills him and finally takes over his entire villa and going out to kill Jack Slater and Danny. He is also responsible to the death of Slater's cousin Frank.
In the police of LA, John Practice helps Benedict but gets killed by Slater after Danny's arrival to the movie.
How he Died
Benedict came to his (Vivaldi's) own swimming pool and finally Benedict pulled out his own gun and shoots Vivaldi which finally being dead and Benedict is takes over his house.