The Punishment for Treason
To accomplish this 20-point achievement, you need to find the traitor and bring him to Al Maulim. During Memory Block Two, consult your map and look for the eavesdropping icon, which will lead you to two suspicious characters. Sit nearby and listen to their conversation. You'll learn of a pickpocketing opportunity across town, which in turn leads you directly to the traitor, Masun. Attack Masun in a dark alley to claim the achievement.
The Blood of a Doctor
This 25-point achievement involves killing Garnier de Naplouse in Acre. Through intel reports, you learn Garnier becomes vulnerable when treating patients. Wear a white robe to blend in with the local scholars, allowing you to sneak close to Garnier and stab him. However, be sure to avoid angry men in the crowd, as they try to instigate fights and ruin your cover.
The Blood of a Merchant King
You have to kill Abu'l Nuqoud in Damascus to earn this 25-point achievement. Find Abu'l standing on a second-story balcony. Use a structure at the southwest corner to climb up to the second story, where you have to defeat some archers before proceeding to the roof. From there, drop down on Abu'l and kill him with your hidden blade.
The Blood of the Scribe
Killing Jubair Al Hakim in Damascus also earns 25 points. Find Jubair burning books. Climb to the building's roof to view a cut scene. Jubair dresses like his followers to try and throw you off his trail, but he appears on your map as the most southeastern assassination icon. Track him to his location and wait for him to face the door before stabbing him with your hidden blade.
Enemy of the Poor
Not every achievement involves as assassination. Grabbing and throwing 25 harassers can earn you an easy five points. Whenever you encounter a pesky female beggar, grab her and toss her aside to eventually earn your reward. This achievement only works with female beggars, not the mad men roaming crowds.