I just used the video from http://www.360-hq.com/Call_of_Duty_4_Xbox_360_Achievements-4...
I did make some changes though. I always got killed by ignoring the guy in the bathroom, so I knifed him before shooting the guy on the other side of the meeting room and throwing a flash.
Then I kill as many as possible while running/crouching along the left side of the seats, didn't wait in cover like the video. Used the gun I started with and the pistol.
Instead of tossing a flash in the next room where the side of the plane blows up I just hid behind the first set of chairs or behind the wall on the right side. While in cover reload. Mop up the rest of the enemies and cautiously advance to the stairs ready to kill whoever comes down.
Toss a flash on the right side of the stairs as seen in the video and duck to the left to clean up the enemies.
Throw the third flash into the next room after reloading. Shoot while you run and toss your last flash into the hall. Run like mad, killing anything in your way, and be ready to line up your headshot with the pistol. You have about 3 to 5 seconds to line up and shoot no matter what time you got to the doors.
All in all this takes a lot of luck and knowing what you need to do before you do it.
This probably took me 5 or 6 hours to do once I was serious and that's after taking a year off from playing COD ^_^. I did do the One Shot, One Kill mission on veteran to remember the button layout before attempting this though.