Both solutions are valid, but I tried both to no avail. If these solutions don't work for you, try this one. I've tried it out 4 times, and it's worked for me every time. It's absolutely weird, but it works. These are classic games, so the classic solutions still work (Like the level select code in Sonic).
In the options menu, set the difficulty to HARD. This provides more enemies to shoot in-game.
Set the Max. amount of lives to 7 (That's the maximum).
Stay on the UPPER LEFT or UPPER RIGHT corners of the screen. When you get to either upper corner, fire continually. Every 4 shot is a pair of homing missiles that will hit 2 enemies.
Don't stray from there or you will get shot. Also, don't hover very much. You can if you want to get a couple enemies with homing missiles, but you increase your chances of being shot down.
You may lose a couple lives on the way, but nothing serious.
The halfway point is a large tank. He has 4 guns, as well as a homing missile-esque gun. Keep to the corners until the missiles start shooting. What I did was stay on the top of the screen and strafed back and forth to avoid the shots. There's a rhythm that you should be able to figure out. The main thing here is not to get over-whelmed. It gets crazy.
When that's over, go back to the upper corner. You should be able to get to the aircraft carrier no problem.
Once you get to the carrier, the view switches to "Top-Down", and you can only strafe side-to-side. Shoot whatever you can, and try to avoid getting shot, and you should have this achievement without frustration.
Classic games have classic solutions, they're sometimes strange. Hope this helps. I've done this achievement for myself , my brother, and a couple of friends; all on the first try. Trust me on the hard difficulty setting.