You do NOT have to play through the game once to unlock hard difficulty just to face him on the 1st mission. This achievement can be completed during Mission 13 on your first playthrough on Normal difficulty.
***POSSIBLE SPOILERS TO FOLLOW***
After completing the minimum objective requirements for Mission 13, you'll get a cutscene of Strigon Team coming to engage Garuda Team. Pasternak orders the remaider of his team to withdraw so that he may face Garuda alone. He will intercept at a very fast speed, and he utilizes several high speed enemy UAV drones to keep you busy as well.
I agree with SpectreSubZero that the F-16 is not the plane for this engagement. I used the F-15E, but only because it was the plane I had selected for the mission, thinking it would be largely air-to-ground focused. I would not recommend the F-22 either because I find it stalls through high g turns often, though its QAAM missiles would probably be very effective against the UAVs.
If I had to do this again I'd choose the F/A-18F with it's multi-target air-to-air missiles. It's got the speed and maneuverability you'll need to keep Pasternak and his UAVs in your sights, and you'll be able to lockup multiple targets for a missile shot.
- Try to keep this fight in the airspace between SteelGunners (Airfield) and Marigold (Ship/ESM). Being able to land to repair damage and reload will be useful, as will the active ESM out over the water.
- The UAVs seem to have trouble at higher altitudes
- Allied Attack is your friend!