gameluver2006

It depends on who you've got in your arsenal. The first time I beat the game, I actually used Slippy (ha!). Everyone says he's not a good pilot, but with his high sheilds and powerful Plasma Shot, he did pretty well. He's available in the following levels: Goodbye Fox and Fox and Krystal. But the best pilot to use is Panther. You won't get him until Star Wolf Returns. Panther doesn't have much on shields, but his laser shot rocks!
Anyway, on to your question.
You'll start out facing off with the Arrow Head. Attack the various parts of it until they fall off. The parts will attack by firing energy rings after falling, so be careful! Anyway, when you've done all this, the head of the Arrow Head will face you and some of the pieces will surround it (I think 8). These pieces will fly at you, and Rob will tell you to shoot them. Instead, focus all you're fire power on the head, barrel-rolling to avoid the damage. It will take several times to master this, so don't get discouraged! Once you defeat the Arrow Head, it is on to face the Emperor himself.
Start out shooting the three orbs that are rotating around him. Once they are all red, his little bobber on his head will be exposed. That's the weak point. Attack it furiously. It will take several times to take him down, but soon, he will begin summoning big pillars to hinder your flight. Just fly to avoid them while firing wildly, and you're bound to hit them. Some other things to watch for:
He will try to suck you in, just like Andross did in 64 and Adventures. Put on your brakes fast.
If the orbs have green rays of light comming from them, avoid those. If all three lock on (they will turn red when locked on) then they will hone in on you and hit with a lot of damage.
Hope that helps, and sorry it's so long!