Petrified

Obtainability
Teleport to the Forest map.

Go through the area with Doggy's tent in it.

You should see a group of four cabins; A cabin with a green roof, a cabin with an orange roof, a cabin with a purple roof and a cabin with a red roof. The cabin with the green roof should have a purple safe in it, just so you can verify you're looking at the correct cabin.

Now, go behind the cabin with the red roof. There will be a skull there. Touch the skull and you will get the Petrified badge.

After you touch the skull, you should get the Skull Lady skin.