Sequence 03, Memory 08 -- The Mentor's Keeper

Head back to Galata to the Assassin's HQ to start the next memory -- The Mentor's Keeper -- which is Sophia's Memory from reading the map.  To obtain 100% Synchronization for this memory you will need to rescue all of the civilians -- and to do that you will need to kill very quickly so that you clear out the first group of Templar and can head right for the red dots on the screen.

There are three white-circles on the radar map that mark locations of groups of Templar and some citizens you need to rescue.  You need to kill all of the Templar at each location quickly, then move on to the next.  Once you have cleared the threat against all three locations you will have fulfilled the requirement for 100% Synchronization.

Replaying Altair's First Key Memory

Now you need to head to the marker to trigger a CS in which you confront the Assassin (who is really a Templar) who betrayed you.  He makes a threat and then closes the gate to the fortress.  You now need to make your way in and exact revenge while remaining undetected for the most part.  Start by scaling the wall to the right of the now closed gate, then when you get to the crenelations stay below and move to the left until you can do a ledge-kill on the patrolling Templar up there.

Altair's Memory - Saving the Mentor

Now take the stairs on the right and assassinate the three guards along the way, before jumping to the bar and swinging down to the roof below and doing an air-assassination on the traitor, thus saving the Mentor.  You now get a CS in which all of this resolves and you learn that this was a recorded memory from your ancestor.