Dark Albion is unlocked once you have completed the credits level of the main game. Dark Hobbe Cave is the fourth level of this second playthrough.
Simply come in first by collecting more coins than your opponents, it doesn't matter which path you take. You can do this in single-player mode with the AI picking up the other player slots. In which case it's probably best not to chose the mine path, as the AI sometimes plays exceedingly well at the minecart minigame, which is worth 10k coins in Dark Albion.