Note: this strategy involves causing accidents more than necessary most likely (I simply love doing this - I managed to kill every character in the level New Life with an accident without blowing cover, firing a shot, or leaving evidence). It is still a great strategy.
During this level bear in mind that the masses on the street cannot see you - you can pull out your gun right in front of them and nothing will happen in the game or to your rating. Start off by following the red crow wherever he goes, without letting him see you. He'll eventually turn into an alley (if he doesn't, you should consider restarting). When you're near a dumpster (but not visible to the main street) either sedate him, or grab him as a shield and quickly knock him out. Quickly take his clothes and put him in a dumpster. Then take his briefcase and proceed to the alley on the far left side of the map where a piano hangs.
You should see a climbable obstacle course that begins with a grated wall, all the way up to the winch where the piano hangs. Place a mine here, climb back down, and wait for a woman dressed in a blue crow outfit to walk under it, then detonate. When the two men in the alley run away to fetch a policeman, run to her body and pick up her SLP40S and her walkie talkie.
THE FOLLOWING LETS YOU GET THE SG552 AND HAVE MORE FUN (if you don't care, simply go upstairs with the briefcase and push the man out the window when no one is looking or poison him and dump his body in the container):
Go to the building on the far northwest corner of the map. Your red bird suit will get you access to this building. Once inside, head left and go up the stairs. Do one of the following:
1) When the guard upstairs goes inside the upstairs room, go to the side of the door. Wait for him to exit, close the door and follow him sneakily, and either sedate him or whip out your pistol, use him as a shield and knock him out. You'll soon throw him over the rail.
2) Leave your suitcase somewhere he can see. When he goes to pick it up, take him hostage and knock him out and leave him at the top of the stairs.
Which ever you choose, take his clothing and weapon. Dressed as a dumb yellow bird, you can now walk around with an MP9 unholstered, which will make using human shields very easy to accomplish. Grab the downstairs guard in this way (he'll let you walk right behind him, though he'll turn a bit), take him upstairs, knock him out. Go in the room with the target, and grab him when he isn't in front of the window. Knock him out, bring him to the second floor landing and throw him down the stairs, along with his guards. Get his Desert Eagle and walkie.
Take the SG552 and briefcase with diamonds to the door near the side exit and set them down for the time being. Equip your MP9. Go outside. THe two big bird guards will cycle. As one leaves, the other comes towards your door. Grab him, and kill him like you did the others. Do the same to the next guard as he comes back (though check your map to make sure no cop will see you). It will take longer to get him inside and throw him over, and you don't need to kill him (you could sneak by him with the SG552 to put in the ICA case, though this allows the next part of my strategy).
Go out to the front, get behind the door guard, make sure no NPCs can see you, grab him, take him inside, go upstairs, and then send him back down a lot faster than he came up. Go back outside, and grab the policeman as he goes into the alley, and bring him back into the same building, and send him to meet his maker by way of a quick drop and a sudden stop. Take his clothing and gun (cops can go anywhere brandishing an SLP40).
Note that the restaurant the last guy is in changes each time and is random. Killing him is easiest if you don't feel the need to set it up as an accident. If you must do this however, you can usually sneak into whichever restaurant he's in through the back, sneak into his room (use your map to time your lock picking and movement), knock him out, and throw him over the rail on the inside staircase.
On the Bluesy Bar, this is the easiest, and you can even get an additional 3 accidents just for fun (The waiter kissing the girl at the top of the stairs can be delayed by walking in front of him as his girl proceeds freely, then grabbed when she's far enough away and knocked out to be killed later. The cook can easily be grabbed and brought to the same place, and then the garbage boy from the same room. If you kill them, the last target will hear it and it'll be hard to dispatch him).
If you must kill the last target by an accident, and the back staircase isn't an option, be very careful not to be seen on a balcony, as this will cause a policeman to come running upstairs to tell you off.
I have yet to find an effective way to obtain the Kazo TRG without killing all NPCs in the level (easily accomplished with a knife or M4). Killing the crowd with mines is always a good one.