These achievements require that you perform a total of 1000 headshots. Both multiplayer and campaign headshots count towards these achievements. However, due to the lack of online community and relative ease with which you can get headshots in campaign, you should focus there.
After playing the campaign, the best spot I have found to grind this achievement is on Mission 6: Manhunt. Play through the mission as normal. You will come to a sniper rifle that is mentioned by your partner. Be sure to pick it up for later. Progress further through the mission until you come to the black loading screen. Just after that loading screen, there is a sniping section where you are overlooking a courtyard from a broken building. Around 15 enemies will spawn in succession as you attempt to protect your partner as he moves across the courtyard. All of them will be standing still at some point so wait for it. Line up their heads with the zoomed sniper and take them out as fast as possible, as if you are too slow your partner will kill them.
There are three guys that spawn immediately when the scene starts. Three more spawn out of the alley on the right. Then one on the far balcony. As your partner advances to the fountain, one will spawn right under you and two from the far corridor straight ahead. Two will jump out from behind the truck on the left. And finally two will spawn on the upper balcony at the far end of the courtyard. As soon as you kill both enemies on this balcony at the end, pause and reload the checkpoint.
You wont be able to track how many total headshots you have grinded, but they all will count behind the scenes. You should be able to get 10 to 14 headshots per attempt of the checkpoint, which takes around 75 seconds to complete. This will earn you 400 to 560 headshots per hour. If you always try to get headshots while playing through the campaign, you really shouldn't have too much additional grinding to do at the end. Not more than one hour.