@kims @BobDevney πλήκτης has the sense of brawler, but not quite the same as “bully.” The adjective θρασύς comes closer as it connotes insolence or arrogance. If you want fancy, θραςύδειλος isn’t bad, although a coinage from Aristophanes isn’t the kind of thing you’d use in normal prose.
TLDR: I’d probably go with “thrasocracy.”