Ok So I compleated every save the citizen in Poor Part Damascus and didnt get the achievement after my first Assassination. Should I also have went to the Rich side and saved the citizens? I'm lost.
There are two other parts to Damascus. You've got to save the citizens in those parts before you get the "Defender of the People: Damascus" achievement.
It means you can't access every part of the cities at the beginning of the game. Each section unlocks as your progress further through the game. And since citizens are in each part of the city, you won't be able to get the Defender achievements until near the end of the game.
I finished the game last night. Each city has three parts, a rich, middle, and poor section of the city. Each part has citizens to save. You get the achievement after saving everyone in every part of the city. So roughly around 30 per city. If you didn't save everyone the first visit to each city, you can do it on one of your later visits. You have 9 assassinations to complete, 3 cities and 3 districts in each, thus your 9 trips.
As a side note, when you save the citizens make use of the mobs that help you in that area. Later in the game it helps when being chased, to run to this area, and let the mob control the number of attackers coming at you. It also makes it easier to assassinate them from behind with your blade.