First, complete Sir Gavin's campaign to unlock Luna's campaign.
Then, start Luna's campaign and clear the visible enemies from your kingdom. Once your lands are clear, there's no penalty for ending turn : use this to get gold and build tile upgrades.
If you capture villages in the East of the map, build at least one Spirt Drill : at level 3, this gives Spirit Essence (green barrels), which will save you time in chapter 2. It's also worth upgrading a couple of Witch's Towers (forest) and Scrapyards (fields), to help in chapter 3.
Otherwise, there's no need to get bogged down conquering lands : a couple of castles and a couple of each upgrade will be fine, and makes it easier to keep those lands clear of enemies.
In battle, use your commanders where possible (rather than ballista or magic), to level them up for later in the game. Aim to get Luna to level 2 by the end of the chapter.
Once you've reached your father's castle (Haüntid Haüs), you'll be sent to three spots around the map to find him. After that, the Grim Reaper sends you to a 'Greening' Undead Field between Haüntid Haüs and your original castle.
Stepping onto that green Field ends the first chapter and gets you the achievement.