Błędnie: There was a battle in the street but before the police arrived one of the men escaped, leaving the other guy with a black eye. Poprawnie: There was a struggle in the street but before the police arrived one of the men escaped, leaving the other guy with a black eye.
"Battle" to 'bitwa', 'walka' 'walczyć'. Słowo to odnosi się do działań militarnych i zmagań w sensie metaforycznym, np. The sailors battled against the storm for a couple of days. "Struggle" to 'bójka', 'szamotanina', 'bić się', 'walczyć'.