The Best of the Best
You'll obtain this achievement once you've completed the final mission "Dust to Dust" on Veteran difficulty.
If you're a previous player of any of the Call of Duty games and their Veteran setting, then this shouldn't cause you too much trouble. Take note that the game still has the same rules as the previous as in for a cutscene or your AI members to do anything, you have to advance forward. If you just stand there, not moving forward, the enemy forces will just keep on spawning, so take your time but move up when you can.
Take note that you must also play the "Prologue" on Veteran difficulty to unlock the "The Big Apple" achievement. Not doing so will not unlock it after you complete the "Hunter Killer" mission.