Once you have recruited an Assassin you can send him on missions from pigeon coops or Assassin Towers. To send an Assassin on a mission you must first select a mission from the contracts menu, then press to assign it to an assassin. Once you have done this you must press to send him on a mission.
You will notice that there is a bar at the top when you select missions this is the percentage chance that the assassin will complete the mission. The higher the percentage the more chance of him completing the mission. Remember to keep it as close to 100% as you can because if you don't, there is a chance the assassin could fail and die. An Assassin can also die in combat helping you so you must be careful with them.
Missions only take 10 - 20 minutes so you won't spend much time waiting and this Achievement should come pretty quickly, once an assassin has reached the level of Assassino you must return to the Assassin's hideout for an initiation ceremony the Achievement will pop after this.
The XP for the ranks are as follows -
Recluta: 0XP
Servitore: 10XP
Assistente: 30XP
Milte: 80XP
Discepol: 180XP
Mercenario: 350XP
Guerriero: 600XP
Veterano: 1200XP
Maestro: 2000XP
Assassino: 3500XP