Assassin's Creed II/Sequence 8: Necessity, Mother of Invention

You have petty much all the skills and tools you're going to get at this point, so further sequences generally consist of working with your allies to take down another target on your quest to eventually get to the elusive Spaniard.

Birds of a feather
This is another following mission, so stay well behind your targets and stick to crowds and benches, but keep a line of sight. When the Templars take a path blocked by guards, get around them by hopping from the wall next to them to the small pier beyond via a pole sticking out of the water. From there you can continue to follow the targets behind the guards' backs. When they make their way into the next plaza, blend with the first group you come to as the Templars meet up with the rest of their friends. They're a little suspicious, since you've gone around killing a bunch of their allies, so they'll try to stay on the move. Keep following them to listen in on their conversation.
 * Memory start: Enter the white marker next to the well outside the Santo Stefano.
 * Reward: 3,000ƒ, Assassination contracts unlocked

They head straight through a guarded arch to a small bridge across a canal, so go through the archway next to it, just to the west to keep an eye on them. When they've crossed the bridge, hop along the beams to their bridge to continue tailing them. After they go around a couple corners, the Spaniard shows up and joins their party. Keep following them as they leave the courtyard to the north. Make sure you hold the unarmed hand button while you're walking near the guys with crates so you don't draw any undue attention by making one of them drop their load. Eventually they will make it to the Rialto bridge and the memory will end.

If at first you don't succeed…
Antonio will follow you, so run over to the Palazzo Ducale in the south of the city while Antonio talk to you. Enter the white marker you'll find out in front of the palazzo. You'll need to check out a couple places around the palazzo to formulate a plan for getting inside. Your first stop is in a narrow alley across from the main gate. From there, head around the south of the palazzo and over a bridge to a tower you'll need to climb on the side of the water. Antonio needs to make it up as well, so if he falls off and dies, you'll have to restart the memory. If you take a leap of faith down from the tower, make sure you wait for Antonio, because you'll desynchronize if you get too far away from him. Next, head north and then back west when you reach the memory wall. This should take you to another white marker next to a cart behind the palazzo.
 * Memory start: Talk to Rosa inside the Palazzo della Seta.
 * Reward: 3,000ƒ

Antonio likes to die here if you don't take the expected path, so try and follow the indication you get from the brief look up to the roof. Start by free running up the cart with white sheets on it to a hanging platform leading to a wooden platform with bundle of wood tied up on it. Jump from the bundle to a higher platform, then to the next platform to your left along the next wall. From here, take another wood bundle up to the next platform where you can finally climb up to the roof. Head over to the white marker by the metal fence to the south.

Nothing ventured, nothing gained
You don't really have to do anything – just crash the glider and end the memory.
 * Memory start: Knock on the door to Leonardo's workshop.
 * Reward: 2,000ƒ

Well begun is half done
Your mission in this memory is to take out the soldiers guarding a few different locations so the thieves can set fires there. The first is close to you, just to the east, but the rest are farther east and south. The close group consists of two brutes standing together on a small footbridge. Simply walk up to them and do a double-assassination while making sure no other guards are patrolling nearby. The next closest targets are two more brutes patrolling around a ship on the water, a little farther west than the rest of the targets. If you head straight there from the previous target, you can swim to the back of the boat and climb up. Whichever way you get there, simply run up behind them and use another double-assassination, although a roving patrol on the dock and the easiest path to the ship being guarded, make swimming both faster and safer.
 * Memory start: Automatic (knock on Leonardo's door if you didn't accept the memory when it was first offered).
 * Reward: 3,000ƒ

Next head to the group of targets in the north. These are three archers on the rooftops that can all see each other. They're fairly easy to dispatch, by either doing ledge assassinations or just grabbing them and throwing them off the roofs. Head south to the next target, which is another brute soldier walking around by some arches along the canal, with guards blocking the entrance next to the footbridge. Swim up to the ledge under where he stops at the edge of the canal and perform a ledge assassination. The last target is also a brute in much the same type of area, just a couple bridges to the south. The difference is he has no additional guards (because there's no treasure chest there), so you can just run in and assassinate him, rather than swimming up.

Infrequent flier

 * Memory start: Enter the white marker on a rooftop near the Thieves' guild.
 * Reward: 6,000, Codex page

You'll want to head due east to the palazzo, following the fire icons on your minimap. If you want to kick an archer, fly toward him and lock on and Ezio will take care of the rest. If you take a look at your large map, you'll see that there is a big gap between the fires in the west and the fires in the east, where you're going. While it may seem the best route is to follow the path to the south and cut east across the shortest distance, the fires along that route are all on the ground. Fly instead to the north where the fires are on rooftops and you'll have the elevation to make it across to the northernmost fire on the east side of the gap, which you'll see is a burning ship on the water. From there you can turn south toward the palazzo and eventually land on the roof with the white marker.

Once you're on the roof, you'll need to make your way into the palazzo without alerting the guards. If you head over to the side of the roof overlooking the inside of the palazzo, you'll see the white marker on a ledge below you to the northeast. Even though you're in a restricted area, the guards take a while to become alerted when they see you, so you can just go down and start taking them all out by running up to them and assassinating them if you want. To get right to business, head down the ladder going over the side of the roof, and when the guard below the white marker gets to the lower landing of the stairs he patrols, swing over the pole to the north to another platform. From there, simply jump over to the platform with the white marker.

When you get into the Doge's apartment, you'll find you're too late and Carlo Grimaldi is framing you for the death. Jump out the window and run down the stairs to Carlo and assassinate him. The guards aren't automatically aware of your position, but it's easy enough to escape them after Carlo is dead by free running up one of the carts with white sheets to the upper walkway, then hopping the railing on the west side below where you came down from the roof and climbing back up. Once you're up on the roof, head to the southeast corner and take a leap of faith down into a hay cart. The yellow portion on your minimap is the area you have to get outside of, so just run a little distance to end the memory and the entire DNA sequence.