The Hidden Blade Assassin's Creed in Depth

Eagle Strike

Start off by taking a fast stealthy path. Run to the left of the docks (shallow water, no swimming necessary). One of the guards there can see me, but you don't have to worry about getting into open conflict. After that continue forward, keeping to the edge of the restricted area. After climbing up a cliff turn right along the edge. Running up the low hanging tree will lead you to the cliff where the scene starts. There are two guards patrolling, so wait until their backs are turned (or just double kill them) to get past anonymously. If you are aiming for full synch, go behind the house right behind William Johnson, or skip the cinematic.

For the Eagle Strike climb the house in front of you and wait for the scene to end (if you skip the cinematic or start from the last checkpoint you spawn at a default location). The setup after the scene allows you to stay on the roof until the assassination. Shoot the two previously mentioned patrolling guards with the bow (guns will alert all the enemies in the area, which can ruin the assassination). You being detected will cause the target to flee. Wait until he reaches the right place to perform the Eagle Strike.

Now for the kill itself. From standing on the roof a fall to the ground below the cliff is high enough to cause death. Most of the cliff is just far enough away that you can't jump past the edge, but luckily a small part of it is closer.