Meet Lance Vance at the bridge of Starfish Island and then he'll give Tommy an M4 Carbine to start the shootout. Walk closer to the garden at the left of Diaz' Mansion until Tommy sees the main guards. Use a sniper rifle or M4 Carbine to finish off the main guards. Keep going along the side of the mansion and turn right to get to the back of the mansion. There will be a few guards along the way - finish them off.
There is a big garage-shaped entrance at the back. Go inside and walk along the right side of the swimming pool. Enter Diaz' mansion and go up the stairs. Kill a few guards while doing so. When you see an entrance at the third floor of the mansion, take it and go through a small indoor maze, killing a guard while doing so.
Go into the main room with Lance behind you. Diaz is in this room. Kill all of the guards and approach the stairs. Tommy will confront Diaz. Finish off the last guards and follow Diaz into his room. Use a minigun or your most powerful weapon and blast Diaz with it. Diaz has armor so it may take a while.
Diaz exits his room on his stomach. He is coughing and injured. Tommy and Lance take out some Desert Eagles and ask Diaz for his last words. Two Desert Eagle shots fly into Diaz and Diaz dies in a white flash, leaving Tommy, Lance, and Ken with the mansion.