The tropht is part of the games "long tale" and requires you to complete two quests to unlock it.
The first is "The Fate of Tsushima"
*** Spoiler - click to reveal ***This is the mission to decimate the forces of Castle Shimura to free it from occupation. Fairly simlle storm the keep battle with all your allies, very similar to the of Castle Kaneda. Linear path, you can't really get lost.
The second is "From the Darkness"
*** Spoiler - click to reveal ***A stealth based mission where you have to poison to vats of Milk to kill all the Mongols, meaning not throwing the lives of your men away. The easiest way is to follow the suspended ropes across the rooftops once you've reached the survey point on top of the tower. The climb to the top of the tower is fairly easy, but don't use the ladder on the inside, use the actual roof to climb up to it.
This mission allows you to kill, unlike all the other ones previous, but make sure that no one can see the Mongol you are going to dispatch.