You'll enter Mad Batter Cave via its second, secret entrance. The other entrance just leads to a dead end. Bomb the north ...

Instead, head to the wooden peg in front of the house and pound it, then drop into the well. Inside, bomb the north wall and ...

To round things off, you can also pick up bounties, which are optional mini-boss track-and-hunt quests, and treasure maps, which require you to sleuth out concealed chests across the Living Lands.