Fun demo once you get the controls the way you like (and more importantly, switch the camera to the mouse-look one).
Ok, first run to your left immediately upon starting and look in the alley down that way to grab the sniper rifle. Then wait for the pedestrians to pass the alley and go back out of the alley and just to your right to the end of the street the limo just drove down originally and pop off the bad guys at the very end of the street with it. Then throw it away because if anyone sees you with it they'll get mean, or go tell the guards. Now you pop into the main alleyway and knock off the driver, change into his clothes and stash the body in that open sewer thing. Then you calmly walk over to the car and plant the bomb. It took me a little while to figure out that the reason you can't plant it normally is just because you aren't close enough to the door...get right up against it. After this just walk off to a safe distance where none of the guards will stare at you, and use the trigger to blow it up once the last guard gets in and the only one left is next to the car. You have now completed all your objectives so go back to that car you started in front of.
No need to get blatant about killing people, the best way is for nobody to ever see you carrying any weapons.