When you are in the beginning of the game look for a guy named Mark and he should have a shotgun.
Wait until he dies and take his shotgun then run up the stairs, when you do the case "Backup for Brad" in the food court climb up on the boxes and get up to where Carlito is.
Hide behind the wall just enough so your shotgun sticks out, when Carlito gets close shoot him as many times as possible with your shotgun.
He should be dead in 3 or 4 hits depending on where you hit him.