The videos are excellent here, but I just wanted to add a tip that made this a cake walk for me.
At the beginning, run up to him and unload on him while he stands still (he'll do so at the edge of the screen, extreme left or extreme right). When he speeds up and starts pulling a COD: WaW and spamming grenades, simply move to the middle of the screen and let him come to you.
Then, jump over him and shoot him in the back JUST ONCE as he moves side to side. Rinse repeat.
The grenades will generally miss you (as will he) and the odds of you being hit is greatly reduced. You may need to veer slightly to avoid the odd grenade, so be a little vigilant. Once he is dead, achievement unlocked.