As usual, there are many ways to carry out the mission. I am going to concentrate on doing it through stealth and silence. The strategy below might seem overly laborious and long-winded, but it's the best way I could find to ensure that the walkthrough works for you.
Specifically, I am going to avoid grenades and molotovs until the very end. This is because explosions sometimes raise the alarm and sometimes they don't. And sometimes, the alarm causes the sidecars to leave (thus failing the mission), and sometimes it doesn't. I have been unable to establish the exact circumstances when each of these happens. So, I am going to play it safe. That said, if you find that you can get away with causing a commotion here and there, go right ahead.
I am also going to infiltrate the buildings to take out the soldiers inside (the alternative is to draw them all out, by raising the alarm). My method is tedious and painful. But I feel that it is easier. If the soldiers are drawn out, they tend to position themselves aggressively, making it harder for you to kill them. Once again, go with whatever works for you. For example, as some others have suggested, setting up anti-personnel mines outside the building doors works very well too.
Getting past the first sidecar
Get your Sapper to step out a little (as shown in the screengrab). This will attract the mechanic nearby. Punch him and tie him up. Then, go inside that area and knock out and tie up the other guys there (three mechanics and a soldier). Be careful to avoid the eye of the officer (shown at (A)) and the sidecar to the right (not shown in the screenshot). Use your cigarettes to draw in and gag the officer too. Alternatively, you can go over to (A) when the officer has his back towards you and knock him out. If you are going to leave his body lying around, be sure to strip him naked. Then, if you wish, you can pick up the goodies at (B) (not compulsory). Return to where the Sniper is.
Crawl your Sniper on his belly down the map, and over to where a cow is grazing. From here, snipe at all the soldiers you can see, starting with the ones closest to you. You should get a total of 7 kills (five soldiers, one mechanic and one lieutenant). Then, run your Sniper over to the entrance of the house nearby (where the lieutenant was standing).
Taking up a sniping position
From now on, most of the action will be at the Sniper's hands. You can forget about the Sapper until you need him. Also, always look through doors (using the "Examine" mode) before entering a room or a house. I will merely say, in the walkthrough, something like "enter the room and kill the soldier inside". I'll assume that you know how to time it right.
Usually, soldiers in a room will be pacing up and down. You have to look through the door and find the right moment when they have their backs towards you. In many rooms, you have to wait quite a while (upto 2 minutes) for this to happen. Be patient. There is no time limit anyway. Also, your view through the door is limited. You won't be able to see the whole room. If you can't see a soldier in your view, wait and observe. They will cross your view sooner or later.
Enter the house, move through the levels and kill the enemies one by one (as shown in the screenshots). You can either truss them up or shoot them (with a rifle; don't waste your sniper bullets inside the house). Don't worry - gunfire won't attract anyone outside a room. Remember to climb up the ladder to the attic and dispose off the officer there too. Lastly, go out onto the walkway and knock out the enemy sniper (and take his bullets).
Enemy at the gates
Lie down on the walkway and take up a sniping posture (position (C)). Check that you have at least 10 bullets (if you have followed this walkthrough, you will have 18 left). From your position, shoot the officer as shown in the screenshot. This will draw a lot of other guys to that spot. Put a bullet into each of them. You should be able to get 10 enemies (including the officer) this way. For your reference, I have marked each of these 10 with a green "x" over their heads in the screen capture. Then, from the same position, shoot down Guys #1 and #2.
Then, go down to position (D) (back down through the house). Standing at the base of the pole there, shoot #3 (an enemy sniper), #4, #5 and #6. Go and pick up the goodies in the crate at (E) (from here, you can actually shoot a couple of enemies inside the buildings through windows, but never mind, we'll tackle them later). Climb up the pole at (F) and perch yourself on top (i.e., when you reach the top of the pole, click and select your sniper rifle). From here, snipe down #7 (another enemy sniper), #8 and #9.
Inside the houses
Enter the two buildings (doors marked (G) and (H)) and kill the soldiers inside. Be careful when going up to the second and third levels in house (H). You can't see much through the doors, so be ready to face the enemies. Remember to pick up ammo from the crate at (I) on that level, and also bullets from #3 (who's lying dead on the balcony outside).
Finishing up
Once you have finished the people in buildings (G) and (H), move your Sniper over to the entrance of the arch nearby (as shown in the screenshot) and lie down. From here, shoot soldier #10. This will draw out #11 (a lieutenant) and soldier #12. After sniping them both, shoot down #13 also (lieutenant).
Then, climb up the ladder nearby and pick up the bullets from sniper #7 whom you shot earlier and is lying dead there. Right next to him is a door (hard to see; look at the arrow in the screenshot). That room has a soldier and a ladder leading to a crate. Enter the room, kill the soldier, grab the items and come back down to the ground.
Now it's time for some Sapper action. Bring over your Sapper and throw gas grenades to knock out that battalion of soldiers nearby. While they are passed out, throw molotovs to cremate them.
Pick up the stuff in crates (J) and (K) if you want (although, at this point in the game, you are nearly done, and won't have any use for them). Go over to the door marked (L) and enter the building. There are three levels with one soldier each. I am sure you are an expert at it by now, so I am not providing screenshots. The third level has a ladder going up to another crate. Take it if you like.
Enter the building next to crate (K) (through door (M)), kill the two soldiers inside and go out into the courtyard. There's a cabin accessible from here (door (N)). The last soldier is in there. Kill him. Finally, run over to the three sidecars and send each one up in flames. Hurrah!