The keys to this trophy are: avoid letting the assassins detect you as best you can, avoiding civilian kills, and making liberal use of Dark Vision and the zoom function.
The first room contains 3 assassins and a civilian. This one is relatively straightforward to do without being seen. If there are 2 assassins directly in front of you, just shoot them relatively quickly and sneak up on the third. If they are spread out take your time and pick them off one by one.
In the second room there are also 3 assassins and a civilian. It can be difficult to shoot any of them without alerting the others. If they come looking for you, there is a bookcase on the left side of the first room right before you enter the second. If you Blink up there it is easier going than staying on the ground. Shots from their crossbows are a lot less damaging than their swords.
In the third room with the 5 weepers and civilian, Blink up to the bookcase to the right and pick them off.
The fourth room gets a little tricky. Activate Dark Vision before entering the room to see which two doors contain the assassins, so you do not kill the civilian.
In the fifth room, look out the window to the left to see one assassin with a hostage, and one repeatedly climbing a staircase. The latter is tricky. You need to shoot slightly in front of his path so he will walk into the bolt. Hit to activate zoom (and to zoom in further if needed), and take them both down.
The sixth room contains 2 more assassins to kill. One of them is walking between the columns in the middle of the room, and the other walks back and forth near the back of the room.
Finally in the seventh room, there is currently a glitch that can allow you to run straight ahead and jump on top of the wardrobe to the left of the final door. You will pass through and not need to kill the remaining assassins. It is possible though that this glitch will not work and you will need to kill the last 3 assassins. If this happens or if you would rather kill all 20 and not use a glitch, there is 1 on the main floor and 2 on the walkway above when you enter the room. Much like the second and third rooms, if you get into a situation where the enemies are trying to engage you, Blink up to the top of a bookcase so you are out of the range of their swords.
Thanks to Coopafication/Coopa Bruzz for the use of this video: