After defeating Fahook once he goes into the back of the plane, when you get him very low on life he will drink from his bottle. At this time you should shoot the bottle out of his hands before he gains too much life. Doing this three or four times will destroy his bottle. Finish off his remaining life points and watch the intermission sequence.

Use the manual aiming to shoot things. When you are on manual, you can aim at the bottle. You will need to do this three or four times. When the bottle is shot off Fahook, you need to make Fahook go near the open back part of the airplane. Once there, shoot him and Fahook will fall off and die.