The Hidden Blade Assassin's Creed in Depth

This video is based on the clever strategy by KaiyuiKurosaki to disarm Rodrigo Borgia by using the smash attack.
http://www.thehiddenblade.com/how-wield-papal-staff-against-rodrigo-borgia
Stabguy illustrates this strategy in a video:
http://www.thehiddenblade.com/disarming-rodrigo-borgia-papal-staff

This video shows a greatly simplified process to obtain the heavy weapon for the smash attack. Most importantly, the player can retry this part of mission if anything goes wrong.

Start by poisoning a Brute in the back of the room, then make your way to the front of the room while blended. When the Brute falls to the ground, he drops his weapon. Stab Rodrigo Borgia with the hidden blade or shoot him. After the cutscene, go back to pick up the dropped heavy weapon. Lock on, fully charge the smash attack, and let it rip. Now that he is disarmed, Rodrigo Borgia is extremely easy to defeat. Just pick up the Staff and mash the attack button until the next cutscene.

After the cutscene, pick up the Staff again and go down to the Vault. As you approach the pit, turn left slightly. The goal is to reach the edge of the pit that is directly opposite of Rodrigo Borgia. When you approach the edge, Ezio will teleport down to the pit to start the next cutscene, leaving the Staff behind. If everything works out, the Staff will then fall into the pit when Ezio teleports.

Defeat Rodrigo Borgia again to start the next cutscene. A new Papal Staff is spawned in the middle of the room. Go find the other Staff on the floor, and kick it around until you can take a nice picture with both Staffs by your side.