the title is very apt for the play as Miss Hardcastle stoops to the level of a barmaid to conquer the object of her love, that is , Marlow. As Marlow is not comfortable talking to woman of status so he doesnt look at Kate while conversing with her. She could not win his favour as a woman of rank. So she stoops to the level of a barmaid with whom Marlow has no problem talking. He falls in love with the barmaid not knowing that she is Kate.He in the end kneels down to beg her love.Thus Miss Hardcastle conquers by stooping. she has stooped , no doubt but rises triumphantly in the end. Thus the title is justified.