The Hidden Blade Assassin's Creed in Depth

Blitz Assassination
Start off by selecting the smoke bomb from your weapon wheel. That way you can throw down the bomb while maintaining your momentum as you run straight through the guard post. Emilio notices Ezio as he approaches, and he calls for his guards ("Guardia!). This automatically puts Ezio in Open Conflict with the guards in the palazzo about a half second later. But by then, the kill animation has already started, and there is nothing that can interfere with the assassination once the kill animation starts. So... technically, this clip is an "Anonymous" blitz, but it sure doesn't feel like it. Part 2 offers a more satisfying "Anonymous" blitz:
http://www.thehiddenblade.com/emilio-barbarigo-assassination-variety-pac...

Stunt Assassination
Emilio doesn't step out to uncovered areas much, so there are few opportunities for aerial assassinations. Emilio will venture into the courtyard briefly right before he is about to board his boat. He even pauses for a few seconds, just to make this assassination a little more convenient for you.

Air Assassinations
From over the courtyard
Move the body of the agile so that Emilio does not see it. Beware of the guard near the window where I left the body.

Emilio's sight extends out 15 m in front of him, so wait for him to start walking back before you position yourself on the beam. Once you get a lock on Emilio in the courtyard, don't wait too long before killing him. If I had waited a split second longer, Emilio would have been out of range for this air assassination.

From over the gate
This clip shows a different way to get into the compound. When you jump over the gate, be sure to hold the left stick up so that you land with a roll. Otherwise, you'll take some damage.

This air assassination is the way the Prima guide recommends to complete this mission. However, the air assassination is relatively short, so I prefer other ones.

From the roof
Swim to the dock of the palazzo. Carlos' boat isn't really there; you pass right through it. Say hi to Carlos as he leaves. Despite my best efforts, I can't figure out a way to kill Carlos in this mission. If you stand in his way, he'll gentle push you to out of his way - even to the point of pushing you into the water if necessary.

If Emilio detects you, he will call for his guards ("Guardia! Guardia!") and run around the inside of the palazzo, which gives you new opportunities to air assassinate him. The problem is that all of the guards in the palazzo also become aware of you after Emilio calls for them. They may interfere with your air assassination by chasing you or throwing stones, so I find it convenient to kill them all first.

After Carlos leaves, wait until Emilio is more than 15 m away before killing the guards, so he doesn't see the dead bodies. After all the guards are dead, you can show yourself to Emilio. Note that you remain Anonymous (white border around the mini-map) because nobody is left to respond to Emilio's plea for help. As Emilio runs around, he will likely run across the upper balcony, where you can air assassinate him. I like to do this from one of the towers for dramatic effect, so I watch him to see which direction he will take across the balcony. Once you see which way he goes, you can climb up the appropriate tower for this nice long-range air assassination. Use the mini-map to time your jump.

Ambush
You can ambush Emilio as he leaves for his boat. You can even board his self-sailing boat for awhile. If you hang off the side of his boat, you will travel with the boat as it moves. If you climb on top of it, you'll slide off the boat unless you walk with it to keep up. When the boat is in position, hide around the corner, just outside of his view. Run out to stab or poison Emilio just before he boards his ship. If you want, you could even wait for him to board his ship before killing him... but (strangely) you will be desynchronized when you return from the Memory Corridor dialog. You'll then be returned to the last checkpoint *before* the assassination, as if it never happened.