I stuggled with this achievement but I finally unlocked it today!
The easiest method for me was to start the game in classical, level 1 (Duck Island).
I used the red plane on the top row which has the homing missile as its weapon.
I then would just fly right low to the map, back and forth and let the homing missiles do there thing.
Once round 2 and 3 are over there is a blue plane in round 4. This is a harder round as the blue plane is better than the reds.
Just keep low and take it out and then follow the same plan for the rest.
Round 5 there is 5 blue planes. I flew along the bottom and kept shooting, then when I reached the end I'd turn, shoot 3-4 missiles then turn back. This way, the blue planes would never come on my screen.
Round 6 there is a lot more going on.
You only need two planes in this round so I just targeted two red ones and then the achievement popped up.
Try to keep an eye on your multiplier score. If it stays on 9x you know you have not been hit.
Hope this helps you out.