The Hidden Blade Assassin's Creed in Depth

Easy and Robust
Port Authority may be the most difficult mission in all of AC2. This is a nice easy way to complete the mission for those having difficulty.

Swim out to the bow of the ship, then turn to swim along the south side of the hull. Climb up the side of the ship, and climb-leap to reach the rail of the quarterdeck. Pull the guard over the rail when he passes. Wait for the other guard on the quarterdeck to leave before you climb up on deck. Use double hidden blades on the 2 guards next to the helm. Hop up onto the rail, look down, lock on, and air assassinate.

Silent Authority
The goal is to wipe out all of the guards stationed around the pier and ship without being seen at all (no yellow/red SSI bars). Here are some notes:

1:26 Keep your distance from the north side of the ship as you swim out to the bow. This allows you to avoid detection from the north-facing guards on the ship. There aren't any landmarks in the water, so use the GPS to gauge when you need to turn. When you reach the ship, keep close to the south side of the hull so that guards cannot see you.

1:45 Ezio's position along the rail is critical when he pulls the guard over. You will be spotted if you pull the guard over the rail from a position much different from what is shown. You also need to wait until the guard is stationary before pulling him over. (I cut it really close in the video.)

2:06 After killing this guard, wait for the patrolling guard on the main deck to turn away before going over the rail. Kill the patrolling guard on the quarterdeck, and quickly use the double hidden blades on the pair of guards next to the helm. These 2 guards may spot you the instant you kill them (see 5:56). Sometimes you'll get the yellow SSI bars, sometimes not. I'm not sure why.

2:18 Run to the back corner of the quarterdeck so that the patrolling guard on the main deck does not see you. Be sure to keep a few inches back from the rear rail of the ship, otherwise the archer on the pier will see you. Air assassinate the archer when he turns away.

2:42 Climb back to the quarterdeck of the ship, and lock onto the last patrolling guard. Back away after locking on, and shoot the guard. Since you are not within view of any guards, you will remain Anonymous. The other guards and the target will inspect the dead body. Some of the guards may leave the ship to search nearby hiding places. The assassination target and the Brutes never return to their original stations, but the other 2 guards do return to their stations at the bow. Wait for an appropriate moment to start climbing the rope ladder so that nobody sees you. This won't always be possible; a Brute sometimes remains facing you after inspecting the dead body (see 6:36).

3:22 Lock onto one of the guards before climbing all the way up. Shoot this guard when you reach the top of the mast.

4:05 Climb down the rope ladder on the other side at an appropriate time, and repeat the process on the other guard at the bow. Keep in mind it may take some time before this guard returns to his station. Sometimes the guard slips and drowns himself at the pier, so you may find that the guard never returns.

4:45 One or both of the Brutes typically stay in front of the bench next to the pier, as they had searched this hiding spot earlier, and then never return to their stations.

5:15 You typically don't get much opportunity to see what this target looks like. If you are curious, use this opportunity to take a closer look.

There is no pier
It looks like Ubi learned a lesson from "There is no spoon," which is an assassination mission that drowns Dante Moro and Silvio Barbarigo by despawning the ship that they stand on:
http://www.thehiddenblade.com/dante-moro-and-silvio-barbarigo-assassinat...

Such an assassination doesn't appear possible on Port Authority, as the target nevers seems to drown while on the ship, regardless of how far you are from him. However, the pier indeed disappears when you are far enough away. You just need to lure the target to the pier first.

This mission is a lot like the previous one. The main difference is that you spare the archer on the pier temporarily; you'll use him as the bait to lure the main target onto the pier. Lock onto this archer as you climb up the rope ladder, and shoot him when he isn't standing close to the edge of the pier. (After shooting him, you need his body to stay on the pier, not fall over into the water.)

Air assassinations
Lock onto the target as you climb up the rope ladder. You can air assassinate from many different locations. If you climb to the top of the main-mast, you can do a spring-loaded air assassination. This is also possible from the fore-mast. You can reach the fore-mast by jumping from the main-mast as shown.

Anonymous Blitz
The Anonymous Blitz for this mission can be found here:
http://www.thehiddenblade.com/bonfire-blitz