Negotiator is the campaign mission Persona Non Grata run backwards from the building where you get the assault drone up to the beginning room where the helicopter crashes. There are 35 hostages, and you are supposed to save as many as possible. The longer you take between stages the more hostages the baddies will execute. There are 4 breach-and-clear sections, and more than one hostage is right behind a captor, so you can't simply shoot the enemies, you have to wait until the right moment, or get their legs first, or something like that. You won't fail if you kill a single hostage, but if you kill more than 5 or so hostages yourself, you will fail the mission. I'm not sure if I'll ever get the Not On My Watch achievo; seems like you'd need to get a one-shot kill on every enemy and run between every stage.
Black Ice is the campaign mission Down the Rabbit Hole and the Spec Ops mission Fire Mission, but the snowmobiling half takes place on the road that circles around the mine down to the building you come out of at the very beginning of Fire Mission. It's fairly easy on Regular, but on Veteren I had a hard time even getting off the snowmobile. You basically have to kill everyone while driving in order to make it. And to get the A Baker's Dozen achievement you just need to slow down and go in reverse back to where there are guys standing to run them all over.
This is probably the diamond mine that Black Ice and its ilk are based on, in Mirny Russia: