Unlocking this achievement will also unlock Dwarves as a playable race.
You receive the required quest in Hildabor, the Dwarven Fortress. To enter via the gates you'll need at least 1,000 gold. They won't take it, they just don't let you in if you're poor. You can also enter via a hidden staircase on the third level of the Caves, but this staircase can also take you to the Undercity instead.
Once in Hildabor you'll receive a quest from a female dwarf to retrieve her earrings. They were apparently stolen by two giant men in the mountains.
The earrings can be found in the Barbarian Camp in the mountains. I've cleared the Barbarian Camp various ways. You can defeat the Barbarian leader to receive them, once I rode in on a Bear that I got from the forest (using the picnic basket) and they were just completely impressed by me and gave me the earrings, etc. I'm sure that there are various ways.
Bring her back the earrings and she'll propose marriage.