to defeat someone in a contest or competition in a way that does not cause permanent damage but makes them look foolish or inferior
Most are so fed up with this new tax that they are threatening to give the Governmentmore than a bloody nose in the forthcoming by-election.
to damage the other side in a war or conflict enough to cause it to withdraw, at least for a time
Giving the national army a bloody nose is one thing. Taking on its full might isanother.