The only way to become an ace pilot is to shoot down large numbers of hostile aircraft. This page contains information on how to win aerial fights in Ace Combat 7: Skies Unknown.
Dogfights are about maneuvering your aircraft in such a way that would allow you to get an enemy's back, preferably while flying in the same direction and on similar altitude. Thanks to that, you can be sure that your missiles will hit the target. This maneuver also gives you a great opportunity to use cannons (provided you get close enough to your target). If the enemy keeps disappearing from your view, switch to another one. Usually, you will have a better opportunity to shoot.
The green vector in the middle of the screen will help you maneuver your aircraft in the right way. This vector informs you about the position of your target. However, the most important thing here is your plane's maneuverability. Dogfights are mainly about making tight turns while decreasing your speed until your machine stalls - use light fighter jets instead of heavy attack aircraft. In missions where you have to destroy aerial targets, remember to select a fighter jet and equip it with parts that improve mobility.
You can also use long-range air-to-air missiles that can eliminate targets before you enter the dogfight mode. Choose a special weapon that can target multiple enemies at the same time to eliminate groups of drones.
If your missile missed even though your targeting system in your HUD was red, you were either too close to the target or the distance and angle between the approaching missile and the movement direction of the target were simply too small for the missile to be able to hit the enemy. More details in Why missiles don't hit the target despite full targeting? chapter.