Lucius Cornelius Sulla is an enormously complicated figure, made doubly so by the fact that we know so little about the man. His memoirs only exist as a few fragments quoted here and there by other, later Roman historians so we cannot be entirely sure what his exact motivations were (unlike those of Julius Caesar in his Commentarii de Bello Gallico or Marcus Cicero in his plethora of personal letters). Nonetheless, Sulla was at his heart a deeply conservative man, one who saw himself as divinely ordained by providence to restore what he saw as a republic teetering on the brink of collapse.

The reforms Sulla enacted during his time as dictator (his official title was "Dictator to fix the constitution", not "Dictator for life" a la Caesar, an important distinction) may have already been on his agenda for his Consulship that he was slated to hold in 88 BC. So when after all the strife and killing of the Marian Civil War had ended priority number one on the new Sulla-led government was to make sure that something like that could never happen again. This was accomplished in two parts: the first part involved neutering the power of the tribunes through legislation, and the second was to make sure that the future leaders of Rome could not repeat (nor need to repeat) what Sulla did. In short, Sulla saw himself as a necessary, temporary leader to fix the Republic, and even offered to explain his actions to the people after he retired, walking through Rome without bodyguards as he was so sure of his safety.

Sources:

The Civil Wars: Appian ; translated with an introduction by John Carter.. New York: Penguin, 1996.

Keaveney, Arthur. Sulla, The Last Republican. 2 ed. London: Croom Helm, 2005.