In Resident Evil: Operation Raccoon City for the PS3 and Xbox 360, the first boss (a transformed version of Dr. William Birkin) isn’t really a boss in the normal sense. He’s a giant behemoth that you can’t beat.
You will notice however that the game tells you to shoot the giant ugly eye on his shoulder to slow him down. Shooting the eye a bit will stun him, allowing you to get away.
You will do this several times, stunning him and running away. Eventually you will get away from him, and progress to the end of the mission.