beat up vs batter

beat up is not a noun while batter is a noun.

Word	Noun	Adjective	Verb	Adverb
beat up	No	No	Yes	No
batter	Yes	No	Yes	No

As verbs, batter is a hyponym of beat up; that is, batter is a word with a more specific, narrower meaning than beat up:

beat up: give a beating to; subject to a beating, either as a punishment or as an act of aggression
batter: strike violently and repeatedly

beat up (noun)	batter (noun)
	a liquid or semiliquid mixture, as of flour, eggs, and milk, used in cooking
	(baseball) a ballplayer who is batting

beat up (verb)	batter (verb)
gather	make a dent or impression in
give a beating to; subject to a beating, either as a punishment or as an act of aggression	strike violently and repeatedly
	strike against forcefully