To perform a Cig Run, you must never use a ration and have the Cigarettes equipped as much as possible. On Extreme, this means you can afford no hits for most of the run. This page has damageless strategies.
The first 3 guards, following the displayed strat should work 100% of the time, unless you run into the guard shooting meryl or take too long to flip them. Should always be damageless. As for the rest of the fight, my favourite way is to shoot the guards 4 times, allowing Meryl to only have to shoot them once to kill them. This is the fastest way I have found that still keeps the Big Boss rank. Another safe method is to just punch them once or hold them in the choke position until meryl shoots.
Start: Many ways to deal with the start, the way I demonstrated is just an experiment. Do what is best for you. 1st Outpost: This one is simple, just make sure to line up for the barrel. For an extra precaution on damageless, shoot the guards once to stun them as you aim between barrels. 2nd Outpost: In my opinion, the hardest part of Damageless. The middle guard should almost never be able to hit you, unless you are rotating clockwise, given this fact, I found shooting only the right and left guard when rotating anti-clockwise and when rotating clockwise, hit the middle guard to avoid him shooting you. It is the only consistent way that I found. Liquid 1: Make use of his ducking mechanic as a breather and to stop him shooting you during / just after I-Frames. Liquid 2: The frame perfect shot is super helpful, but if you don't get it, make sure to be quick on shooting him after the bump. Liquid 3: Same as Liquid 1, just watch out for his 1st shot. Liquid 4: Easiest part, every man and his dog knows about where to aim to get him in a stun lock Liquid 5: Can be tricky, but I find that if you aim between Liquid's forehead and his steering wheel, you will shoot him fine. I kind of jiggle between there.