what is "vanquished inferior" ?

Um--it's difficult to say, without some context, sue. I will guess that you have read this in a story. If that is the case, then the only thing I can think of that it means is that one person or group has been defeated, and that the defeat "proves" that they are inferior to the winner of the battle.

Jackie's hit on it, and she's right about needing context here, for it could have been "they" who were "vanquished inferior"--but it could have been an "it" (say, a concept such as freedom) or "she" or "he" who had been "vanquished inferior"--defeated as an inferior.

I don't know whether Churchill really said this--he was quoted in a grade-B movie I recently saw--but the phrase shows pluck:

"From failure to failure with enthusiasm."