Smackdown
Full armor/health are needed. Across the street from Derrick are two cop cars. You can boost either one. If you look around first to make sure no patrolling cops are nearby, you don't even have to run after you break in.
When you get to where Bucky will be, be sure to back into the marker so that you can come out in a hurry to follow him. Bucky takes a lot of alley ways trying to lose you. This isn't the most difficult chase in the game, although he does go down a lot of alleys. You can take some parallel side streets as long as you stay reasonably close.
When he pulls into the yard of a house, you should pull across the street next to a brick wall. Get out and snipe the guy on the porch, then back the cop car across the street next to the sidewalk. It makes a good getaway car.
Four thugs will be waiting for you inside. Opening the door to throw a grenade just gets you shot up and doesn't seem to hurt them that much, so instead, just ready your automatic weapon and go in shooting. As soon as you have eliminated them, turn and start up the stairs with your gun ready. Bucky will be waiting at the top of the stairs to shoot you. Take him out.
Unlike most missions where gunfire is limited to bad guys, the cops will be all over this one. By the time you kill Bucky, a cop or two may already be in the house. Resist the temptation to shoot him and raise your wanted level even higher. Instead, just run out to your getaway cop car and take off. If you have learned the art of watching your radar and turning the opposite direction from any oncoming cops, you should get away without too much difficulty and the mission is over.