Another grindy and no fun achievement, yay! SUGGESTED METHOD 1
The other solutions are good, but if you are done with Halo 4 and Spartan Ops and still is missing "a few" of them, I've found an easy and calm way to farm them. Easy because the watchers will dodge little to nothing while you shoot at them and also because you can do this at the very beginning of the respective mission. Calm because not one enemy will come after you, so there won't be any firefight distractions.
Load up the Episode 4 of Spartan Ops called Rally Point. This mission happens in Valhalla (again... I love that map but Spartan Ops reused the same maps too much). Go to the middle of the map (where the Spartan Laser used to spawn on matchmaking). From there you will be able to see on the opposite side at least a Watcher, a Knight and a Crawler.
Shoot the Watcher until it blows. Pay attention to the Knight because it will respawn infinite Watchers after you kill the last. If you run out of ammo there is a box of ammunition to the right. I also found that it's best to switch your Battle Rifle for a Marine's DMR since those are more accurate and can kill a Watcher with 5 well placed and timed shots (I was playing on Legendary, maybe lower difficulties will take less).
I got to a point where I could see 2 Knights from afar and they were both switching back and forth which one would spawn the Watchers, so that helped to go faster as well.SUGGESTED METHOD 2
Another good and alternative method is to load up the Spartan Ops mission 9-3 "Science Mountain". You will be given Scorpion Tanks and so it will take 1 shot to kill a Watcher. At the end of this short mission there will appear lots of them. The other positive thing about this method is that there will be a lot of Knights there too, so you can farm those simultaneously. Set the difficulty to easy and your Tank will be indestructible, so your only focus is to kill, never dodge.
- average mission time: 13 minutes
- average Watchers per game: 30
- average Knights per game: 15 (although I was getting more by letting some be revived by Watchers)
If this solution helps you in any way, you're welcome to leave a thumbs up and a comment.