Here is a list of notable achievements for the game, which have you completing some aspects of playing in a certain way in order to unlock:
Absolute Symbiosis - You need to get about 8/9 assassinations and have a complete Synchronization bar; you can do this by saving citizens, visiting view points or getting ranks by Al Mualim.
Blade in the Crowd – You need to kill any of your main targets in stealth, using low-profile and blend in the game so that they are not aware before dieing. You can do this on any of them but it becomes progressively more difficult.
Conversationalist – You must exhaust all dialogues with Lucy, before going resting as you will not get a second chance. Make sure the convo-options are exhausted and she prompts you to go to sleep.
Defender of the People: Acre, Damascus, Jerusalem - Complete missions in the indicated places.
Disciple of the Creed – This is apparently a glitchy achievement and it can still be unlocked by doing all side missions before moving onto assassinations. Officially it’s unlocked by having a full DNA bar after your kills, so avoid combat in a similar way to Blade in the Crowd.
Eagle’s Challenge, Dance, Dive, Eye, Flight, Prey, Swiftness, Talon, Will - To unlock do these, as listed, in order: 50 leaps of faith, 50 combo kills in combat, 75 dead guards by knife-throws, last 10 minutes in combat, assassinate 100 guards, perform 100 counter kills in fights, perform 50 stealth assassinations, defeat 100 opponents without dying.
Enemy of the Poor – You need to grab and throw 25 beggars, or harassers, to complete this achievement. Remember it won’t work if you keep on throwing the same person.
Fearless – Climb all of the 91 high points in the game, press your synchronize button and you’ll unlock it.
Gifted Escapist – Simply jump through 20 merchant stalls to unlock this.
Look here for a comprehensive list of achievements.