Just so everyone knows what a watcher is here is a image:
In the campaign find a spot that has a good amount of watchers, kill the group, kill yourself, rinse and repeat. Your achievement progression will be updated under your Halo achievements (unless its having problems that day).
Watchers are in the Halo 4 campaign, they are a part of the Promethean race so there are none in Halo 1, 2, or 3.
If you want to find more of them you can play in the later levels of Halo 4 so don't focus on them in the beginning levels. Thanks Darklord 1899 for bringing that to light.
When you plan on farming the 1000:
I don't recommend going for this one until after you obtain all Halo 4 achievements but when you do get all the other achievements like me, load up the mission Shutdown on rallypoint bravo, once you fight a knight with a incineration cannon make sure to grab it.
Then right when your supposed to walk into the light that will take your shields away, make sure you set yourself up right when you complete the objective. Here is my video of doing it: