Bad North: Jotunn Edition

For the setting to change to night, you will need to be past the 1st battle of a "turn". It can happen during the 2nd battle if you stretch it out but is more likely on the 3rd battle.

This means you will probably want to try for this achievement early in a new/separate campaign, at the same time you go for Split the Party:

Starting fresh, complete the first few islands as regular, save gold to turn your first 3 commander squads in to infantry (shields).

Once you have 3 commanders set as infantry class, on a fresh turn, look for a smaller island that only has 1 or 2 viking head silhouettes above it. Deploy only 1 commander here and win the island (recommend Easy/restarts enabled).

Once they have won that island and you're back at the map, look for another small island with few enemies that is connected and do the same thing again, deploying only 1 commander instead of all 3.

When you first start the 3rd battle island, you are looking for a bold pinkish hue from the oncoming sunset -- if you see this, then go ahead and deploy.
Here is a screenshot for reference:

You must win the island which means 1 house must survive, and it must be fully nightfall when the last enemy dies.

A good strategy here (if you're playing on Easy) is to back your squad off a bit and let the enemy toss a torch or two at whatever they're attacking before you assault them. This can buy you the extra minutes you need for the sun to fully set.