Port Authority - 39 Meters
The goal in this video is to shoot the target from as far away as possible. You desynchronize at a distance of 40 meters, so 39 meters seems to be the best one can do.
Staying undetected was intended to be a key challenge for this mission, but the developers chose an unusual way to enforce "stealth" in this particular mission. If you transition from Anonymous to Exposed within a certain region around the ship, you desynchronize. However, if you are already Exposed while entering this region, you cannot become Exposed again, and you can thus avoid the requirement to remain undetected.
Start by venturing away from the ship, and become Exposed. Now run toward the ship while guard(s) are chasing you. Note that you remain Exposed, but you do not desynchronize. Attract as many guards around the ship as you can without letting the target see you, and then kill almost all of them. (If you kill everyone, you will become Anonymous again, which means that you will desychronize if you are detected.) Now engage the target and lure him to the quarterdeck of the ship. Kill off the remaining guards by throwing them into the water. This ensures that no weapons are left behind for the target to pick up when you disarm him later.
The target can't be disarmed unless he has been injured sufficiently, for example, with a throwing knife. Once disarmed, he won't have any weapons to pick up. Keep brandishing the sword at him; there's no need to attack - he'll soon become so demoralized that he will run away. As he flees, switch to the hidden gun and start aiming. You'll lose your lock on the target after he's more than 30 meters away, but your aim is still preserved. Fire when his distance is 39 meters from you, and hope that no civilian gets in the way of the shot.
Still Life - Mysterious Death
The goal is to poison the target and escape the scene without anybody seeing you (no yellow SSI bars), and without killing anyone other than the target.
This particular path down to street level allows you to avoid detection. Fast walk between civilians to approach the stairs, and wait for the target to pass. Poison him and then fastwalk to the rail to superblend:
http://www.thehiddenblade.com/superblend-exploit
Go to the top of the rail, turn right, and then turn around. This gives you room to get a "running" start so that you can jump across to the other rail. Take care not to bump into anyone as you jump across the stairs. Use the lamps and rail as shown to escape the grounds of Palazzo Pitti.
Hitting the Hay - Eagle Strike
You need to stay Anonymous throughout this mission. Start by killing the nearby archer, and then shoot the archer on the building across from you. Collect his dead body and move it to the stunt location as shown. As the target circles around the area, he won't be able to see this dead body, so you'll need to place another dead body to lure him there. Move the body of the first archer as shown, but take care to wait for the target to pass by first. This gives the nearby guards an opportunity to inspect the dead bodies first, so they don't crowd around the target when he finds them later. Over 2 minutes later, the series of dead body distractions finally catches the target's attention.
Aim the jump by standing on the tower apex and tilting the camera. Look over Ezio's head to fine tune the aim. When it's time to jump, tilt the left stick directly up and run. Reach behind to make the grab and then air assassinate.
Glad to see you found an application for the "already Exposed" exploit on Port Authority. I've been thinking that FLAE could use it for Eagle's Bruise.