Middle Earth: Shadow of Mordor A New Master Trophy/Achievement will give you one Bronze Trophy or 15 GamerScore points. You need to brand a Captain while in combat to get the A New Master Trophy/Achievement.
To get the Middle Earth: Shadow of Mordor A New Master Trophy/Achievement, you should complete the story mission "Queen of the Shore" and must buy the "Combat Drain" ability.
Completing the "Queen of the Shore" story mission will allow you to unlock the Brand ability and by buying "Combat Drain" ability you will be able to brand enemies during combat, that too without grabbing them.
The spawning of Captains happens randomly all around the map. All you must do to get the A New Master Trophy/Achievement is try and reduce the Captains health till the skull symbol turns green, when this happens, you are all set to unleash your Combat Drain finisher as many times as required.
For those who are still unsure on how to get Middle Earth: Shadow of Mordor A New Master Trophy/Achievement, watch the video given below: