- Don't get into conflict
- Lockpick one door
Start off by following Elise and listening to what she has to say. If you're bored, try to blend in with the crowd at all times. It'll be good practice for later.
Investigate the Area
When you complete your first objective, you'll be standing in front of a building. Head around the left side of it, ducking down the alley and speaking to the wounded soldier. When the cut scene is done, so is your objective.
As you leave the alley with the wounded soldier, look to about your 11 o'clock, or slightly to the northeast. You'll see another alley, and running down it will lead to another wounded soldier on the right hand side. After he points to the direction Robespierre went, head that way and take your second right, just before you reach a carriage parked against a building. Follow that to your third soldier, then climb the wall to the east when you're done conversing. Follow the rooftops to the shaded circle to the south, completing your objective when you arrive.
Stick to the rooftops at all times during the chase, as the ground will almost certainly lead to conflict and failure. It's not easy, but keep an eye on Robespierre via the objective marker, tailing him until you trigger a cut scene.
From your starting position, move to the left and jump across the rooftops. Just off the north side of the building and across the street you'll see a Sniper on a rooftop. Sneak up behind him and take him out with the Hidden Blade, although the game likes to force you into Air Assassinations when on slanted roofs.
Jump across the street and cling to one of the windows on the north side of the target building, then shimmy around (to your right) so you're on the west wall (front). Hang from the wall, then look down and you'll notice three snipers on balconies. When you're ready, drop down and take out the Sniper on the north balcony with an Air Assassination. Don't worry, his buddies won't (shouldn't) notice a thing.
Climb through the window and take cover by the door, waiting for a Seeker to walk by. When he does, kill him with the Hidden Blade, then move in the direction he originally came from. As you reach the end of the hallway, snap to cover and use your Eagle Vision to spot three (one is a balcony Sniper) Extremists in the adjacent room.
If you study their patrol patterns, the three bad guys will split up, with one along the left wall, the Sniper on the balcony and the Brute in the middle. When the patrolling Extremist moves to the left wall, sneak up and kill the Brute with your Hidden Blade, then quickly do the same to his buddy. Lastly, pop into cover behind the Sniper, taking him out with a Cover Kill.
From your position at the window, you should see a room to the southwest that has three Extremists inside. One is a Brute, one is a Seeker and the other is irrelevant because he's half asleep. Take cover next to the door, waiting for the Brute to turn his back to the Seeker. Quickly kill the Seeker with a Phantom Blade headshot, then approach and take out the Brute with a Hidden Blade. Lastly, murder the sleeping (he kind of woke up for us) guard just for the giggles. Oh, you can also kill the balcony Sniper with a cover kill. You might as well, no sense risking him getting wise later on.
The door the Robespierre is right there, but you have more business to deal with first. Pop into Eagle Vision and look to the east to spot a locked door. Head in and pick the lock, but don't go through. There is a bad guy on the other side, but just opening the door will complete the challenge. Now you can head back and enter the room with Robespierre to complete the memory.