The grappling hook is part of the solution in New Jersey. It is in the attic next to where the raccoon appears.
Use the grappling hook to climb the tree and recover some egg shells from its nest. Take this back to Mews, as it provides proof of the Jersey Devil.
Back downstairs. Look out the window.
Get the grappling hook and go back downstairs.
After you get the grappling hook you should see a monster. Go outside and you should see it again. Then go under the tree and click on your items bag and click "use" on your grappling hook. Then climb up the rope and get the egg.
Umm. Probably go inside. There is something you need (a grappling hook) in the attic.
In the New Jersey house, climb upstairs to the attic and retrieve the Grappling Hook. Then come back downstairs.
In a nest at the top of the tree at the old house in New Jersey. You need the grappling hook from the attic to reach it.
When you see the Jersey Devil at the old house in the forest, it flies away. Use the grappling hook from the attic to climb the tree next to the house.
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Dragon Roost Island
On Mansion Row, you can get the $5 bill from the tree by jumping from the hedge or the arrow sign. In New Jersey, you need the grappling hook from the attic to climb the tree to the Jersey Devil's nest.
At the spooky house in the New jersey forest, slide the dresser over to the left so that you can jump into the attic. It is only a raccoon up there, but you can find a grappling hook that comes in handy outside.
When you see the raccoon in the attic, keep going right and you will find a grappling hook and rope. When you come down, the Jersey Devil will fly away and you can climb up the tree with the rope.