As the description of the conquest already says, you have to kill 5 enemies with air vehicles in Gulf of Oman, which can be an attack helicopter or a jet.
-I recommend doing it with the helicopter because it is easier to fly
-Try to fight enemies on the floor and especially against tanks that can have up to 2 players together
-Go to the flags that are being captured, sometimes there are enemies on foot, which makes it much easier.
-Receive a shot from Stinger, it seems strange but when you don't know where the enemy is, you can put the camera in 3rd person and see where the shot came from.