My strategy for this mission was to take out as many as possible using the tech in the alleyway.
To do this, I'd run and grab a car and beat them to the alleyway. I'd park the car anywhere on the street, it doesn't matter where - you're not using it to block them.
Directly across from the alleyway is another walking area with some concrete gardens etc on the sides, you can hide behind one of these. From there, hack the cameras until you get to the one that's in the middle of the alleyway, you should be able to see the convoy coming.
Once the convoy reaches the alleyway, you should switch to the camera that overlooks the exit. When the lead car nearly reaches the exit, bring up the blockers. The lead car will back up over a transformer (?) in the ground that you can blow up - do this, blowing up the lead car.
Quickly switch to the rear cars and blow the devices near them. They should get out - one of the drivers will be carrying a cellphone you can explode. Do this, and it should take out the rear car and block the knock-down targets in. If you have trouble with this, plant some IEDs beforehand and use those.
From here, you'll have to shoot your way out. I was able to just wait for them to come to me and I could take them down with an assault rifle. The two knock-down targets waited in the alley, and I just had to sneak up close enough using cover to knock them down.
Apart from jammers there isn't much you can do to stop the scans. As you may have already noticed there is a small indicator telling you the progress of the search right under the minimap. If this bar reaches 100% the police has located you and you have to get out of the search area ASAP. The bar goes up whenever you are in an active scan (jammers can interrupt this) and it will slowly reduce its % as soon as you leave a scan area. Once it reaches 0% the scans will stop (there are some exceptions). Sometimes escaping the police can be easier than escaping the scans (you can perform takedowns on cars while the scan is an "invisible" enemy) but then again there are some missions where the scans will just restart.
For escaping the scans The most important thing isn't really speed but vehicle handling. With the fastest car ingame you could technically outrun a scan but usually they just place another one right in front of you as soon as you leave the previous scan area. What really is key is maneuvering the car fast. Make sure you take a road where you can cut alot of curves. Usually there won't be more than 3 scans active at once and if you zigzag you shouldn't have too many troubles escaping all of them. If you really have to run through one (let's say there's a scan right on top of your mission destination) you can still use your jammers.
Best Answer
Some of the storyline missions give you a reputation bonus for completing them with minimal bloodshed. But considering that these aren't repeatable, they are not a sustainable way to fix your reputation.
The best way to do so is to prevent crimes. Note that you get a greater reputation bonus for both taking down the criminals before they hurt the victims (but not before the "Crime propability" bar turns red and the "Suggestion: Intervene" HUD message appears - you won't get any reputation bonus when you scare away the criminal too early) and for performing a melee takedown on the criminal instead of just killing them. There are three different ways to notice crimes:
You are more likely to find the latter two in areas with a high density of moving pedestrians, like parks or the promenades near the water. The pedestrian-density seems to be higher during the day than at night. Also keep in mind that none of these events happen when you are currently on a mission.