You will need to have pacience
After you encounter the two Sukhois that fire cannon rounds, Shark 4-6 will dogfight the right Sukhoi. It bled its speed and stay behind of Shark 4-6. You have to look to the rear of the F/A-18 and follow him. The Iranian pilot will try to fire his missiles multiple times.
Every time that he tries to shot, your pilot will tell you: "He is tracking" "Enemy Lock" 'Dump Flaires" You can dump flaires when he says "Enemy Lock" or "Dump Flaires" or "Flaires Out,"Flaires Out". It´s an advertising to you. In a moment,your pilot will manage to stay behind him and says "Lock´em up Hawkings". When you lock the AIM-9 missile in him, WAIT ,because he will deploys several flaires to mess up your aim.
If you already plays at multiplayer,the best way to shot down a fighter or a helicopter is fire the AA missile or the SA-18 Igla or FIM-92 Stinger after the enemy pilot deploy his last flaires,because the missile will not find countermeasures;it´s the same thing at these mission. And the pilot helps you one more time: He says "You get tone",it´s time to fire your missiles! He also says: "Guns! Guns!",when he says it,you have to switch to cannon and fire its rounds. Note that,when he says "Guns! Guns",the enemy Sukhoi is very close to your airplane.
Note one more thing: if you miss a missile,the trophy will not appear,you have to restart the entire mission again.