This achievement is currently only possible in Utopia Builder as the Story Mode requires you to explore the Frostland. "Colonise the Frostland" ambition is also out of the question. Which is why we only have two viable options: Develop a Metropolis or Build a Prosperous Future

I have tried "Develop a Metropolis" but it does not work due to hitting resource bottlenecks to sustain a population that big. Remember you only have ONE steam core so you cannot access unlimited resources.

The trick to this achievement is to select "Build a Prosperous Future", i.e. collect 100,000 of each resource and eliminate all problems in the city. It is a race against time as your resources are limited and you don't want to use them up. Select the easiest difficulty. I recommend foragers vs machinists so you get optimal buildings to research.

Select Horizons or Crater map, I did this on the Crater one as resources are close by and you get more coal. Build houses and start to frostbreak to access every resource. Don't even bother with oil or steam if you have it. You'll want to complete this achievement before or right after the first whiteout.

Raise funds as soon as you start the game, don't worry about factions and relations on this one, you'll be done with the playthrough before it is relevant or game breaking.

Build a council hall and research institute asap.

Sign laws that increase production or decrease demand of your resources. You can also go for Allow Productive Outsiders if you need workforce.

Research a mine, a sawmill, a hothouse, a factory and a goods factory. Later you can go for charcoal plants if you run low on coal. Try to pick the one that yields more output unless you're using too much heat or are getting too much disease. Later you'll want to research a hospital and a filtration tower if needed. Housing insulation and heat recycling is nice to have too.

Now watch as your resources accumulate. The biggest bottleneck at the start is lack of workforce so be sure to place those hubs accordingly, you'll need them anyways to accumualate all those resources. Expand the districts and build everything you've researched. You can dismantle the research institute once you're done to save on heat and workforce.

Use the steam core for either more goods production or advanced coal production.

Build more districts and upgrade them to increase output. Use emergency shifts liberally.

Now the weather is getting colder and your growing city requires lots of coal. Turn off the generator or turn on overdrive. It is ok to have bad conditions for a while if you're far from done, just don't let it get worse than notable. If you don't finish before the storm, turn off that generator during its entire duration to not use up all your coal, some will die but it's worth it.

Now you've probably accumulated all resources but need to solve city problems. Build some hospitals and perhaps filtration towers and voila, that's your achievement complete!

This achievement is best done on citizen difficulty in Utopia Builder with the prosperity ambition. You must stockpile resources in a race against time. Scouting the frostland is not allowed so you must find a way to efficiently gather everything before your city uses it up.