专 (zhuān): To monopolize or to take sole control. Think of “specialist” (专家) - someone who has sole expertise. Here, it means monopolizing power.
横 (hèng): Unreasonable, perverse, harsh. This is a special reading of the character. The more common reading, `héng`, means “horizontal.” In this idiom, `hèng` carries the sense of being brutish and going against reason.
跋 (bá): To trample upon or to travel over rough terrain. It implies stepping over boundaries, rules, and people without a second thought.
扈 (hù): Arrogant, unbridled, or unrestrained.
How they combine: The four characters create a powerful image. `专横` (zhuānhèng) describes someone who monopolizes power (`专`) in a harsh and unreasonable (`横`) way. `跋扈` (báhù) describes the behavior of trampling (`跋`) on others with unbridled arrogance (`扈`). Together, `专横跋扈` is a full-throated condemnation of an absolute despot.