Here is the full list of all 11 Bad North achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Complete the campaign on any difficulty
Fully upgrade one of your commanders
Win an island in the snow
Win 3 islands on a single turn
Kill 1000 vikings
Win 10 islands in a row, without losing a single house
Win an island at nighttime
Kill all the vikings in a ship, before it reaches the shore
Purchase an upgrade for one of your commanders
Complete the campaign on hard, recruit all commanders and keep them alive
Kill 15000 vikings