You need to complete this before he reaches the end or you have failed. The trick is not to shoot at him at the start of the chase. Doing so will just waste bullets and have you starting over. Instead wait until he reaches the second set of bars Or pipes then fire you will know if you hit him due to the fact he will flicker and take damage. Repute the same action until you hit him 3 or 4 times he will fall to his death and you will be able to move on. This stage is all timing and watching for the flickering cue. After the first successful shot you should get the timing down as when to fire and when to wait. This level will take a few times to get past. However, after he is hit for the first time the pattern is easy to learn and it's exactly that a timing pattern. Shooting him right away will cause him to flicker but take no damage. Use this to gauge when to start firing when he starts to take damage you have the pattern down and soon he will fall like the wimp he is.