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.
Kill 15000 vikings
Complete the campaign on hard, recruit all commanders and keep them alive
Complete the campaign on any difficulty
Win an island in the snow
Fully upgrade one of your commanders
Win an island at nighttime
Win 3 islands on a single turn
Kill 1000 vikings
Win 10 islands in a row, without losing a single house
Kill all the vikings in a ship, before it reaches the shore
Purchase an upgrade for one of your commanders