The deck I used to sign the black book of Azathoth with Mark in hard mode.

Running the deck

Fighting

That's obviously the easy part with Mark. With Beat Cop and Enchanted Blade, you already attack at 8, which even in hard is most often enough to fail only on the tentacle. Vicious Blow will save you some actions at the moment when it matters the most, so it still seems to good to pass. I completed with 2 .45 Automatic to be sure I draw a weapon early.

Finding clues

With a poor 2, this is of course a bit more complicated. And with the rather restrictive card pool available to Mark, there is basically no choice:

• Evidence! and Scene of the Crime, while not always easy to time well, are reasonably reliable testless clues. Just don't waste them on low shroud places, and feel free to use Shortcut to bring your new friends from the encounter deck at the right place to kill them.
• After that, Flashlight is still the next best available investigating tool, enabling to clear easily low shroud locations.
• I find the other auto clue cards really too hard to use
• Which means that in most scenario you will still have to find a few clues by really investigating. Typically it will be 3 shroud locations where flashlight is not enough and the events are a bit wasted. By stacking some skills ( Take the Initiative, Perception, Unexpected Courage ), using Sophie and maybe one charge of the Flashlight, you should get some score high enough to have a fair chance of passing.

Staying healthy

Healing cards are usually not great, but are really useful for Mark, allowing him to abuse Sophie to both pass tests and draw while staying in the safe zone from Shell Shock. For example a card like Second Wind actually reads to 'draw 2 Unexpected Courage and 3 other cards' (one now, the other two when you use courage) Hallowed Mirror is a bit slow, but still a life saver, and I often had some time with nothing better to do, waiting for a flashlight or a monster to show and help me collect some proof. Finally Beat Cop and Tetsuo Mori are there to take some damage.

getting some cash

The deck is a bit expensive, that's why there is Emergency Cache and Act of Desperation

Upgrade

Here are the important ones: Emergency Cache -> I've had worse Also gives you two cash, but prevent damage at the same time, and greatly improving your survival. Beat Cop -> Beat Cop still one the best allies available. Enchanted Blade -> Enchanted Blade My favorite weapon for Mark. Big guns are not an option because Flashlight is too important, small guns are just disappointing, Machete is too expensive for 2 xp. There is still Timeworn Brand, but I find it a bit overkill and too expensive, both in xp in credits. So yes you will run out of charges with Enchanted blade. It's Ok. Once in a while you while have to make one more attack to finish an enemy, but the sanity and cards you get from the blade definitely compensate for those few lost actions.

Winging It or Perception -> Ever Vigilant + Stick to the Plan

After that, you could buy Charisma to get both cops out, upgrade Tetsuo Mori to The Black Cat, upgrade Hallowed Mirror to First Aid, upgrade Vicious Blow ...