To "vanquish" means to:

The term "vanquish" specifically means to overpower completely or to defeat someone decisively in a conflict or competition. This word is closely associated with the idea of total victory or complete subjugation, often used in contexts involving battles, competitions, or any scenario where one side achieves dominance over another.

The other choices present different actions that do not encapsulate the essence of "vanquish." Supporting partially implies a lack of complete control or dominance. Negotiating peacefully suggests a resolution to conflict without overpowering or defeating an opponent. Retreating from conflict indicates withdrawal rather than active engagement or victory. Thus, the choice that accurately conveys the meaning of vanquishing an opponent is overpowering them completely.