From Longman Dictionary of Contemporary Englishbattle it outbattle it outCOMPETE WITH/TRY TO BEATto keep fighting or opposing each other until one person or team wins Sixteen teams will battle it out. → battle
Examples from the Corpus
battle it out• Phil Gramm all battling it out for second-and third-place showings.• The Yankees and the Red Soxs are battling it out for the championship.• For the Sunday the pros would be on their own, battling it out for the first prize of £500,000.• They showed no sign of brotherly love as they battled it out for the runner-up spot before the record crowd.• This is why bodies exist, rather than separate replicators still battling it out in the primordial soup.• In Atlanta, 12 teams will be battling it out in two divisions.• From their earliest days they were battling it out - sometimes for the same parts. 