batter vs beat up

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

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

As verbs, beat up is a hypernym of batter; that is, beat up is a word with a broader meaning than batter:

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

Other hypernyms of batter include beat, work over.

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

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