The Godfather: The Game/Execute Emilio Barzini Jr.

''Emilio Barzini Jr. is the new Barzini Underboss. He's holding a funeral for their late Consigliere, Domenico Mazza. Use this opportunity to wipe out the Barzinis once and for all! Emilio is quick and smart enough to flee when he's outmatched, so make sure to stop him before he escapes.''
 * Reward: $10,000 +9,500 Respect


 * Bonus Condition: Take out every Barzini before killing Emilio or kill Emilio with a car bomb (Xbox 360, PS3, Wii)
 * Bonus Reward: $50,000 +47,500 Respect

To take out every Barzini first
You will find Emilio and his men in a graveyard next to a church. Approach the graveyard from the right of it (the south side) and turn right into the alley between the stone wall of the graveyard and the building next to it. As you approach the entrance, a Barzini will emerge. Crouch behind one of the many stone blocks jutting from the wall and take him out. Hearing the gunfire, more Barzinis should appear. Keep killing until no more appear.

Then take cover to the left of the entrance and shoot any enemies you can from there. Then go into the graveyard and take cover behind the stone coffins to the right. Shoot and kill any other Barzinis remaining, then kill Emilio. 

To kill Emilio with a car bomb
In the Xbox 360, PS3, and Wii versions you have to blow up Emilio with a car bomb. He tends to run away from cars into the graveyard, and if you have the cops or a hit squad on your side they may kill him for you. One way to get the bonus is to disregard the instructions above and blow him up at the start of the firefight. Now drive north up the street towards the church and stop near Emilio. Get out, immediately crouch, equip the bomb and drop it. Crouch-walk away south down the street past the graveyard and alley, then get on the sidewalk. The car explosion is usually not sufficient to kill Emilio. So while the bomb timer is counting down, equip an accurate long-range gun like the pistol and weaken him with one or two shots to the knee. The bomb detonation should then kill him outright.
 * ensure your vendetta level with the Barzinis is low (pay off the FBI if necessary)
 * if you've hired a goon, dismiss him