Although "beef" in the colloquial sense you describe is certainly at home among the sort of palookas who might be exploring Lex Luthor's varied grievances against the Man of Steel, the expression is (surprisingly) not 20th C American.
Worldwide Words, a delightful collation of etymological goodies, traces the expression to England in 1725, when one might have heard miscreants (such as Luthor's ancestors) complaining that bystanders “cry beef upon us: they have discover’d us and are in Pursuit of us."
The implication is that to shout "beef!" - or, perhaps to speak of shouting "beef," was originally a kind of rhyming slang for "[stop] thief!"
The article goes on to suggest that the expression evolved into a cry of alarm, thence to a protestation of grievance, and that this figurative "beef" traveled with emigrants to Australia (who raised a lot of beef both with and for their former homeland) before returning and, we presume, crossing the Herring Pond to where Americans in general (not only readers of D.C. Comics) had been waiting to put it to good use.