The text on the achievement actually reads "Saved almost every person in Frostland...".
When sending your scouts out into the Frostland, make sure you accompany every party back instead of letting them find their own way. Then, when the refugee parties start to show up - accept them all, including the sick.
There is likely a number of people you have to save, which I'm not sure what the exact number is, I got this when my city population got to about 350, which was when the first refugee party arrived.
I'm not sure if it's required for this achievement, but I also convinced all the Londoners to stay in that mission.