When I first started this quest I did not like it very much on account i would fire a Suppression charge (the only attack the ship has) and the missile would 50% of the time disappear before it reached its target. After doing the quest day after day I learned a few techniques that i thought might help someone doing it for the first time.
-The Suppression charge has a range of 100 yards, so keep in mind that just because your Turret is aimed on a spear gun, you may be too far away, and your SC will not hit it.
-Aim low, near walls.You don't have to hit the gun, just around or near the gun. I like to aim for the ground but I've accidentally hit the walls near them and it still knocks the spear gun out.
-It is OK to get hit once each spear gun, some you can not avoid but make sure that if you did miss or fire too early that you do NOT move on to the next gun. Ignoring 1 gun can shoot your plane down.
-Just because your SC does not have a cooldown does not mean you should fire it like a machine gun! Take your time when firing, it is better to be late and get hit once than to miss.
Lastly If its your first time running the quest take your time finding each gun. It can be hard to get all 4 soldiers dropped in 1 pass. I dont know if this will help anyone with the quest but noticing these things made it a lot easeir for me.