You set off in a restaurant, following a guy in a red bird suit. Keep track of him - it's easy to loose him with all the crowds out in the streets. His path is somewhat random, he won't be taking the same way each time. You have to sedate him before he reaches the bookstore in the North-Western corner of the map. Do it when he enters a back alley, preferably with a container nearby to store a body. Wear that idiotic costume of his and take the suitcase. Recovering it is an optional task in this mission, so you'll be carrying it the rest of the level.
Enter the bookstore and go to the first floor. Place the suitcase on the desk when you're told to. Don't listen to the guard who orders you to leave. Instead, wait for him to leave (duh). Your first target is here for you to kill. Get rid of him and place the body in a container. Take his radio.
You now have to leave the bookstore - it won't be easy, as long as you want to take the suitcase with you (and you do). To do that, you'll have to get a yellow costume. Wait for the guard to enter the room and sedate him. You don't have to hide the body. Take the suitcase and wear his costume, then leave the building.
The two targets you now have to kill are talking through the radio. The woman is walking around the streets and you should see her on yours map when you're close enough (listen to what they're saying to know where she is). Wait for her to enter a back alley and strangle her. Remember to do that near a container to hide the body, as the back alleys are also being patrolled by the cops. Don't forget the suitcase - if you leave it alone for too long, one of the policemen will grab it.
To get the final target, you'll have to enter the club he's in (it's chosen randomly from among 3 available on the map). The procedure is the same in each case - you first go to the back to find a waiter/partygoer having a break, then sedate (or knock out, it you're out of sedatives) him and take his clothes. You're free to enter the building (remember that as a guest you can't go to the kitchen or so). The birdie you're hunting for is at the top floor. Go there and get rid of him. Grab your suit on your way to the exit.
HINT: There's a fine sniper rifle near the last target, but taking it will alert everyone around, so don't do it unless you're not running for Silent Assassin on this one.