Eagle Strike on Political Suicide Contract
http://www.youtube.com/watch?v=X5o9ftqc53s
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This video shows how to do an eagle strike for this contract from the top of the nearby building. Here are the steps:
1. Get several guards to fight you. This includes the ones guarding the building where the target is. There also is a group of guards walking around.
2. Drop the dead bodies in a line to where you will perform the eagle strike. Save the last body you drop to start luring the target.
3. Climb the building but make sure the target has been lured. There are a few tricks to climbing up the dome which is supposed to be impossible to climb.
4. Climb to the cross on top of the dome and jump from the side of it. You can grasp the side of the building before you hit the ground, then air assassinate the target. 
Not really defensive, since you did call the video great, and you did have a point. I just said that because I was comparing eagle strikes and didn't want to insult the climbing the ranks eagle strike by calling it slow.
But that doesn't necessarily mean the eagle strike isn't as cool, just slightly delayed
Whoa man, no need to get defensive, your video is great. I was just pointing out something, that's all.
"When you have to kill a man, it costs nothing to be polite."- Winston Churchhill
"Kill a man, and you are an assassin. Kill millions of men, and you are a conqueror. Kill everyone, and you
Some eagle strikes are faster than others. On my second eagle strike for Bernardo (from another tower) it just as slow. And also Stabguy's eagle strike in climbing the ranks. But that doesn't necessarily mean the eagle strike isn't as cool, just slightly delayed. Luckily my eagle strike for Francesco was pretty fast.
Yeah, it probably was the game. You might have noticed that there was a higher ledge I could have grasped. It would have been easier, and I could have air assassinated faster but I like falling through the air longer. There were some ledges below the one I used, but I could never reach them. I did notice that the air assassinate took a little longer than usual, but since I got it all in one recording I decided to use that for my video. And by the way, sometimes when I grasp that ledge I hang by my arms so that I could air assassinate only when he's directly below me.
Ah, ok, thanks for that information. I wasn't sure if it was the game itself that was limiting aurlcooljay's speed or if it was a pause on his part.
"When you have to kill a man, it costs nothing to be polite."- Winston Churchhill
"Kill a man, and you are an assassin. Kill millions of men, and you are a conqueror. Kill everyone, and you
Video quality is a little lacking, but I like how you figured out how to climb the dome. That and the eagle strike itself is great, thanks aurlcooljay. 
(This is really a small thing, but in between grasping the building and air assassinating, it seems like you hesitated a bit. It's cool when eagle strikes are all one flowing motion, but it's really a small nitpick. You did a good job)
"When you have to kill a man, it costs nothing to be polite."- Winston Churchhill
"Kill a man, and you are an assassin. Kill millions of men, and you are a conqueror. Kill everyone, and you
from what i can tell, the continuity of the eagle strike is related to how target is positioned relative to how you jump and grasp the ledge. if the target remains in camera view as you grasp and initiate the air assassinate, you can get a nice smooth transition. otherwise, there is a slight pause as the game tries to "find" the target out of the camera view.
typically, if you jump toward the target (but not over), grasp to the side, and then air assassinate, you can keep the target in view and achieve a smooth transition, but this isnt always possible.
there are exceptions... a nice example is aurllcooljays eagle strike on bernardo. ezio reaches behind to grasp a short wall. since the wall is short, bernardo remains in view, and aurll managed to quickly follow up with the air assassinate. i like how the camera angle rapidly spins to keep up with all the action.