It's been a month or two since I've played, and I believe I beat it on normal or whatever the normal difficulty is called.
Anyways, the way I remember beating it is that you do much better if you go at the ships from side to side rather than front to back. That is until you get all of the defenses down. Then you can take out the engines from back to front. I just ignored the planes, having my wingman defend me the whole time.
The most frustrating part is when you have to blow up the cockpit to finally take the thing down. You have to take exactly the right approach or your missiles will miss every single time.
Also, I think I used the F-15 with the multi-air (maybe ground, whichever will lock on to the carrier parts) missiles. Save the multi missiles until after you get the radar jamming equipment down. I think I basically used them to lock on to the engines at the same time after I got tall the other stuff out of the way.
I think the rest of the game after this is well worth getting past this annoying level. However, it's pretty much more of the same if you've played any of the other versions in the series.