This scenario is completely fucked up, I spent close to 20 hours to finish it. The RNG is brutally biased, on the starting screen from 4 survivors scavenging its on average 2 blacks, 1 death and 1 resource.
My solution avoids the recommended use of Shortcut, as it had way too much luck factor needed. No matter if i deployed it on turn 12 or 25, never removed The Wall. I know that with luck it would happen eventually, but to me it felt too random.
Based on my observation The Wall appears between Turns remained 11 and 5. Try to get there using the usual methods (frost, black cards and HP management while keeping resources relatively slim, not to end up with a deck that is too random) and acquire as many cards with the blue eye +2 icon as you can. There are a few, the one that worked for me was Torch - for an investment of Wood it lets you choose your upcoming Place or Event from 2 choices. Once you get to Turn 11, keep playing the card, with a bit of luck you will see The Wall among the next 2 Places, choose the other one and you can avoid The Wall. All you need is to finish the last few turns and achievement unlocks.
I know it is still a bit random, but having a 30 cards deck with 2 Torches, maybe a fire or some other card drawers lets you play them in at least every other locations between 11 and 5, essentially giving you a 50% chance to avoid The Wall. A lot better than the Shortcut.
To get Torches, if you don see them until Turn 15, use the Sceptics Idea boost skill that adds 3 new ideas for one food.