to beat up: to strike a person hard, thrashing or flogging them with repeated blows
This verb is the ordinary Greek word for giving someone a beating. It pictures physical violence done to a person: pummeling, thrashing, flogging. In the New Testament it turns up wherever people are roughed up, whether by a mob, a master, a court, or a jailer. The tenants in Jesus' vineyard parable seize the owner's servants and beat them; the apostles are flogged before the council; Jesus himself is struck in the face while on trial; and Paul, who once beat believers in the synagogues, is later beaten publicly in Philippi.
Behind the word lies an older, blunter image: it first meant "to skin" or "to flay," the way you would strip the hide off an animal (the related noun means "skin" or "leather"). By the time of the New Testament that literal sense has faded, leaving the vivid coloring of a rough, hard beating, close to the English slang "to skin someone alive" or "to give a hiding." It is not a technical legal term but everyday language for laying into someone.
Paul uses it once for effect rather than for violence. Describing his own self-discipline as an athlete, he says he does not box "as one beating the air": throwing punches that land on nothing. Even there the core idea is unchanged, a person striking blows; only the target has shifted from a body to empty space.
The word says nothing on its own about the instrument or the setting. Neighboring words fill that in: one word means to whip or scourge with a lash (μαστιγόω), another to beat with rods (ῥαβδίζω), another to strike with the fist (κολαφίζω). This verb is the general one, the plain "beat" that any of those could be a sharper version of.