Rewards: Pounds: 1000 (+150), EXP: 500 (+150), Extra: Outfit - Master Assassin
Challenges: 1. Kill fewer than 5 Royal Guards.
From the ferry, make your way to the vantage point by climbing the castle walls up ahead. A scene plays in which you're given various opportunities to tackle the given situation. Keep in mind that if you want to complete the challenge, you can only kill a maximum of four Royal Guards.
The infiltration opportunity (Chief Yeoman) and the assistance opportunity (Constable) aren't too rewarding. The idea is that you first kill (or steal from) Chief Yeoman in the main garden, free Constable and then assault Lucy Thorne with the assistance of some Royal Guards. Much more interesting is the unique kill opportunity with help from the Allied Guard, located to the north. To reach him, move over the rooftops to avoid royal guards. Speak with him and he'll explains that he can help you by faking an arrest, bringing you to Lucy without constraints. He adds that this cannot currenly be done because "three guards know my face", which is complete bogus since these guards are not even located inside the main building where Lucy is located, but hey, let's not conflate gameplay and 'story'.
You can actually just kill the fake guards, since these are marked red in Eagle Vision and represent Templars. The first one is in the main garden. You can actually just throw a knife at his head from the building near where you met the Allied Guard. The second fake royal guard is to the east of the area. Head over the rooftops and avoid the royal guards by either taking the lower walkway or simply rushing past them. In any case, from one of the platforms here you can take out the fake royal guard with a knife headshot.
The last fake guard is located on the roof of the main building. Backtrack in the direction where you met the Allied Guard and use the roof of this building to rope launch to the main building. Alternatively just climb the corner near to where the Allied Guard is currently standing (as marked by the skull indicator). Climb the tower for a nice vantage point; the fake guard is patrolling alongside a lot of other royal guards, so a knife headshot is again best. Return to the Allied Guard afterwards and he'll fake your arrest. Simply move around the corner and into the main building's entrance.
Head upstairs but don't come too close to anyone and walk very slowly. Simply head straight ahead, turn right and move between the pillars. Assassinate Lucy the moment you get the chance. Exit the Tower of London and make your way to the waypoint in the distance to finish this memory.