There are 4 different factions. Assassin Guild, Mercenaries Guild, Romanies Guild, and Thieves Guild. The one you will want to focus on is Assassin Guild. This is because you have to do most of it anyways and they are the easiest of them all to complete. There are 3 sets of challenges only containing 7 total challenges to do. I suggest being active with these during Sequence 4, as you will be recruiting likely the full roster of assassins.
Call Assassination during a fight: When you are actively fighting enemies, just press Must have the red bar filled by one.
Call Assassins on a target: Press while not in a fight and assassins will come and kill a nearby enemy. Must have one red bar filled by one.
Use Arrow Storm: Must have all 3 red bars filled (meaning you need at least 5 assassins recruited or not active in missions). Hold down and a rain of arrows will kill enemies on screen.
Call your Assassins within a story mission: You should get this naturally, but during any story mission call them out to help you. You can replay DNA sequences, or just do them in the Master Assassin based missions.
Recruit Assassins: You will likely at one point get stuck on 11/12 recruits. You will recruit a few more and the number will not change. After you have taken over all dens, make sure there is no recruiting icon anywhere. There are 6 memory based recruits, 5 of them you do after taking over dens. The last one is unlocked after finishing Sequence 3 Memory 3.
Train recruits to the rank of Master Assassin: You need to train 7. There is an achievement related to this alone. See The Mentor achievement description for more information on how to rank them.
Successfully perform a Den Defense: You will learn how to take control of a Den in the storyline. As you take them over, some will be attacked if your awareness gets too high in those areas. You then must go contest and defend the area that is being attacked. Each time you rank an assassin to master, they will lock the den from this happening. Therefore, if you lock all dens you will need to replay Sequence 2 Memory 6 until you get the challenge unlocked. Some report it unlocks automatically after getting all Master Assassins. Some also report it doesn't always count and will have to be done a few extra times.