A more serious version of 'no-holds-barred'
Another phrase that's used to refer to an extremely violent fight is knock-down drag-out.
marked by extreme violence or bitterness and by the showing of no mercy
The traditional term is
a fight that continues until one side is completely defeated
When used to describe a serious contest the term "fight to the death" may be used figuratively in order to describe the inability of one party to respond to further attack. In such a case where mortality is not assured then Fight to the finish would be more apt / appropriate.