One thing to note is that Realism difficulty will only be unlocked after your first campaign playthrough. So unfortunately, if you had plans to jump straight into it you'll have to wait until you beat it. I would recommend playing it on Veteran your first time through if you've had experience with other COD campaigns. In total, I'd say you'll be spending a solid 7+ hours on Veteran if it's your first time playing through.
Cutting Heads off Snakes requires all missions to be completed on Veteran. There are 17 missions total:
1. Strike
2. Kill or Capture
3. Wetwork*
4. Tradecraft
5. Borderline
6. Cartel Protection
7. Close Air
8. Hardpoint
9. Recon by Fire*
10. Violence and Timing*
11. El Sin Nombre*
12. Dark Water*
13. Alone*
14. Prison Break*
15. Hindsight
16. Ghost Team*
17. Countdown*
* = Level has achievement associated
I'll be honest, it seems that this campaign overall was more difficult than most. I think that's also due to the nature of a good handful of enemies having armor this time around, thus becoming bullet sponges. For these enemies you'll primary be focusing on headshots. Luckily, 2-3 shots from just about any weapon will take care of them. Not to mention just enemies overall seem they spent quite a bit of time at the shooting range as they were just a tad more accurate than they have been. Their reaction times were just outstanding, and always having that 6th sense of where you are at all times.
As far tips, always refill on ammo and supplies every moment you get. Utilize your flashbangs/tear gas along with your Molotov and grenades. It really can be a night and day difference instead of always being the hero with your guns. Do not try to run and gun. That simply just did not work for me even when I wanted it to.