Surviving the Aftermath

I reckon there are other ways of doing this with different combos, but this worked for me.

Game setting notes
I found it best to make catastrophes common but as short as possible, then boost the animals on the map. Tweak the size of colonists that arrive in groups and their 'quality', as you'll solve population another way. Soil should be barren for the challenge boost, and you can tweak the ratio. Low wood, NOT no wood - you'll need some trees. Overall, tweak the challenge difficulty with slight adjustments until it hits 250% (weirdly though I was paranoid about the wording of the achievement text so I did 255% just to be safe). Importantly, set bandits on the world map to the highest setting, and choose the survivor idealogy. Keep lakes on your map, but reduce to low. You may wish to reload to ensure there's a coastline - easy access to early fish makes for better conditions. Tech can be slow, as too can healing, though be sure to support with medical tents. Anything that doesn't affect difficulty is your choice.

General strategy
This game is 100 days of basically keeping at least 12 adults alive/well and ensuring you have a steady stream of kids supplemented by the survivor outposts on the world map. Keep basic resource generators constructed but bounce workers around as needed. You can set a maximum value for resources at the Recycler, Stock Pile, etc. and folks should automatically move on when that cap is reached.

People will die at a relatively consistent rate - at least, they did for me - but it was constantly balanced with maturing adults and new survivors from outposts. Short catastrophes are easy to deal with; you'd only need a heater or two to keep your tents/tenements heated, and a maintenance depot can keep the house and heater at top condition for the space junk damage. I did have two medical tents with 2 staff each pretty much the whole run. Folks are fragile at this difficulty, so infections and radiation are a problem. Remember - roads roads roads. Keep folks away from pollution.

What worked well for me in this run was a combination of concentrating my survivors in a protected pocket away from pollution, rely heavily on specialist-killed map animals (you'll get the majority of your food this way), slow exploration, and, at times, save scumming. Animals in the region will give you food but also will be frequent threats to your people and specialists - especially sand worms. Use scout towers to slowly reveal, save, then see if your specialists can take them out. Delete unused buildings or scout towers that have maxed out their range. Relatedly, because there are tons and tons of bandits on the world map to kill, you'll frequently have tons of silver to use to recruit new folks. I had 10 specialists by day 30ish and with those specialists you'll get the rest you'll need from fighting bandits on the world map.

As you have specialists coming in, be sure to use the Outpost Depot building to set up some survivor outposts in the world map. Even with bad settings, with four outposts, by Day 40 I had groups of 4-5 survivors (granted, most were elderly - but the elderly still work in this game, so, not a bad haul) arriving every other day.

I didn't push tech too much - I wanted tenements with interior walls so that folks kept the labor force supported with children, and I wanted at least one boosted heater. Remember to set resource caps so a worker doesn't turn all your lumber into firewood.