The last enemy target in this combat level is the aircraft carrier. Before you attack it, you must battle with destroyers, submarines, and enemy jet fighters.
If you watch the radar closely, you'll notice the different types of enemy ships while they are still far away. Aerial targets are indicated by a bright spot while seaborne targets are indicated by a dark spot with a light outline. Lock-on before they approach you and shoot. You can sink them before they get you.
You have to refuel at the mid-point of combat levels two, three, and four. When you see the "Out Of Fuel" indication appear at the bottom of the radar, press the 
button to call a Tanker to refuel you. Using the radar, guide your aircraft into the docking position and get your fuel tank filled, and your missiles replenished. Failure to do so will cause you to careen into the ocean when you inevitably run out of fuel.
It's a marathon, not a sprint[edit]
As the first true combat mission, you will learn what the typical flow of a combat mission is like. It will take some time for you to reach your target at the end of the mission, and there is no way to speed that process up. Your only true objective is to survive long enough to reach the target. To do this, you must a) avoid taking as much damage as possible and b) successfully connect with the refueling tanker in order to fly far enough to reach the target. You're not actually required to engage anything else, although the game becomes fairly pointless if all you do is avoid conflict until you're forced to fight. Pushing down and to the right or left will generally prevent the game from allowing anything to attack you, and the only thing that suffers as a consequence is your score. However, it is possible to play more realistically and still survive to the end of the stage.
Remember that you have two types of attackers to worry about this time; those in the air, and those on the ocean. Your altitude won't make much difference to the airborne attackers, but it can make a difference to those at sea. If you are higher up, it will be harder for both the destroyers and submarines to attack you, and for you to attack them. It will be harder for them to attack you since the horizon will be lower on the screen, giving the game a smaller opportunity to fire at you before they scroll off the bottom. Naturally, it will be harder for you to hit the boats since they will be so small, although lock-ons are still possible. Also note that you aren't allowed to fly below 500 feet. At that altitude, you will be very vulnerable to attacks from boats.
Boss: Enemy aircraft carrier[edit]
All three bosses of Top Gun follow the same basic flow. Once you get far enough in the mission (provided you successfully refueled your jet in mid-air), the game will instruct you that you are approaching the target. Your altitude will be adjusted, if necessary, and you will see the target off in the distance. In this case, it is an enemy aircraft carrier. You will also see the "health" meter of the boss appear in green in the upper right corner of the screen. Your goal will be to bombard the target with bullets and missiles until the target explodes, while avoiding counter attacks from the target, and from accompanying enemy fighters.
Boss targets tend to be a lot more accurate when they fire bullets at you. And they frequently fire missiles at you in groups of twos or threes. Never fly straight at a target; they are guaranteed to destroy you with bullets. Your approach toward a target should be indirect. Moving the control pad in slow controlled circles is one way to take them on. Moving the cross-hairs in a small figure eight is another, more effective approach. Tap the 
button to continuously fire your machine gun, even if you're not necessarily properly aimed at your target. If you still have plenty of missile, tap the 
constantly as well, and don't worry about hitting other targets as well. If you have a low supply of missiles, you should still tap A repeatedly, but be a bit more judicious in your use of B. When you succeed at blowing up the target, all other combat will instantly end, and you will be taken straight to the landing sequence.