To fight it out

from The Collaborative International Dictionary of English v.0.48
Fight \Fight\, v. t.
   1. To carry on, or wage, as a conflict, or battle; to win or
      gain by struggle, as one's way; to sustain by fighting, as
      a cause.
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            He had to fight his way through the world.
                                                  --Macaulay.
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            I have fought a good fight.           --2 Tim. iv.
                                                  7.
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   2. To contend with in battle; to war against; as, they fought
      the enemy in two pitched battles; the sloop fought the
      frigate for three hours.
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   3. To cause to fight; to manage or maneuver in a fight; as,
      to fight cocks; to fight one's ship.
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   {To fight it out}, to fight until a decisive and conclusive
      result is reached.
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