The Hidden Blade Assassin's Creed in Depth

The goal is to empty the Sistine Chapel without being detected. You can use a similar process to wield the Papal Staff as a weapon to kill others; this is shown at the end.

If you haven't seen it already, I recommend first watching and reading this article on the "Non-story Rodrigo Borgia Assassination," which has highly relevant information:
http://www.thehiddenblade.com/rodrigo-borgia-non-story-assassination

Here are some notes on this video:

1:15 After poisoning the first brute, fast walk to the second brute to poison him as well. Use fast walk to leave the area quickly.

1:56 The dead bodies cause quite a commotion. It is useful to leave the area and return in order to reinitialize the room. This clears the room of disrupted civilians, who are useless since they cannot be used for blending. Be sure that the poisoned brutes have died before you leave. Otherwise, they will respawn when you return.

2:40 Disrupted civilians and dead brutes have been removed from the room.

2:54 Use fast walk to poison this brute and return to the blend zone for a moment. Then immediately turn around fast walk to poison the brute in the corner.

3:33 Again, you'll find it useful to clear the room of disrupted civilians. Be sure that the poisoned brutes have died before you leave.

4:40 Line up Ezio with the opening in the partition so that only one brute is in line of sight. Walk toward the opening to attract the brute's attention. Immediately turn around and hide on the other side of the scaffolding. Use the hidden blade to kill the brute as he approaches.

4:58 Repeat on the corner brute.

5:26 Only 3 brutes remain, and they can't see each other. That means you don't need to be stealthy when you kill them. Air assassinate the 2 brutes on each side of the scaffold.

6:00 You'll attract the attention of the last brute when you walk out of the area. Climb up the scaffolding and air assassinate him when he investigates.

6:33 If you wish, you can leave the room and return to remove the last of the civilians and the dead bodies. This leaves you alone with Rodrigo Borgia, as shown in the preview clip.

6:53 You can also leave a brute(s ) alive so that you can kill him later with the Papal Staff. Poison Rodrigo Borgia and wait for him to drop the Staff. Pick up the Staff and walk along the wall toward the brute, staying very close to the wall. You must kill the brute from behind so that he dies instantly. Otherwise, the mission will end with your detection. (Thanks SBIzokronus and Asaic!)

9:10 If there are any civilians left behind, you can kill them, too. Take care not to stray too far from Rodrigo Borgia's body, which causes desychronization. You can kill 3 civilians before you desychronize. You might as well... when you poison Rodrigo Borgia, there is no way to progress the story.