For some strange reason, you can get Silent Assassin with 2 headshots and 1 alert in this mission on Normal and Expert difficulty (I haven't reached this level in Pro yet). Useful, ain't it?
The easy way
You're not actually supposed to do this so simple, but it works: Run straight ahead and see the colonel completely unguarded. Shoot him before he can alert anyone and drag him into the back-alley with the ladder. Put on his outfit and think about all the time you just saved not doing this the way it should be done. but let's pretend this isn't possible and do it the way it should be done.
The Lieutenant's coordinates
When you start, run left and go to the back of the lieutenant's house. Pick the lock and enter in sneak mode. (Two guards standing here making this impossible so not sure how the previous editor made this work?) Have a silenced pistol or fibre wire in hand. Sneak up the stairs, don't walk because he'll turn around to face the stairs, and strangle or shoot the lieutanant before he sees you. Depending on where you stand, the guards will hear the gunshot so fibre wire is preferred (and possible).
Holster the gun, run to his body, take his clothes and coordinates and exit the house before the guards enter. The lieutenant's body will not be discovered, so don't worry. Taking his clothes is actually not advised because the guards will immediately see through your ruse. The Colonel's outfit will however work and even allow you to walk into the house through the front door(on normal difficulty) and out even when the guards rushed in.
The Colonel's keys
Now enter the bazaar if you haven't killed the colonel yet. Go to a spot where no one will notice you with a gun in hand. When you have a clear view of the colonel, shoot him and holster your gun immediately. The civilians will go to alert the guards. In that time window, pick up the colonel's key and go to your exit. You will still have silent asassin rating.
There are a few other possibilities to complete this level: -There is a restricted area to the north and a sniper rifle near its entrance. Not sure what the point is of this, but you might be able to snipe the Lieutenant or Colonel from the roof here? -There are several open windows above the Bazaar from which you can also take the shot without running into guards. You can hide here for the guards to calm down and then collect the Colonel's key with more ease. You can get here by running straight ahead from the starting point, going into the small alleyway to your right and climbing onto the stairs.