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
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The goal of this mission is to kill every guard in the Doge's Palace and Carlo Grimaldi without being seen at all. That means no yellow bars over your opponents.
Most of my videos start at the checkpoint immediately before the assassination mission. This missions starts earlier - at the checkpoint when you land on the roof.
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Ghost
The goal is to kill every opponent you that can reach in the "Having a Blast" (Marco Barbarigo) mission without being seen. That means no yellow bars whatsoever. To keep it challenging, I don't use anything other than the hidden blade. This mission is basically the same as the Silent Crash of Carnivale, but on steroids:
http://www.thehiddenblade.com/silent-crash-carnivale
Here are some notes:
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Silent Night at Emilio's Palazzo
The goal is to kill every opponent in Emilio's Palazzo without being detected. Just for fun, I also stay entirely unseen in this mission. That means no yellow alert bars over the opponents. Also, no smoke bombs and a minimal throwing knives, just to keep it challenging.
You may need to get the first patch for AC2, which was released December 2009.
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Silent Crash of Carnivale
The goal is to kill every opponent you that can reach in the "Having a Blast" (Marco Barbarigo) mission without being detected. There are lots of ways to accomplish this task - this video shows just one way. This video is not optimal, but it demonstrates some of the techniques that can be used.