Take the shells back to the Mews lab and test them. The DNA analyzer will prove the existence of the Jersey Devil.
You need a photo of Nessie at Loch Ness, a tooth from the Chupacabra from Puerto Rico, and egg shells from the nest of the Jersey Devil in New Jersey. (see related solution)
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.
It's not the chicken eggs, it's the egg shells from New Jersey. When run through the DNA testing, the egg shells from the nest in New Jersey prove the existence of the Jersey Devil.
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.
Bring them back to the Mews lab for DNA testing.
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.
Use the grappling hook that you found in the house by the raccoon and hook up to the branch.
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.
The proof for Nessie is a photo from Loch Ness. The proof for the chupacabra is a tooth from Puerto Rico. The proof for the Jersey Devil are egg shells from its nest in New Jersey. You cannot prove the Yeti, but when you have proven the other three, you go to follow Bigfoot, which is a similar creature. (see the related questions)
You will find a rope inside and you can get the egg shells from the nest of the Jersey Devil. Then you can prove it exists. You still need to get the photo from the Himalayas and also prove the Loch Ness Monster and the chupacabra. Once the three are proven, you will be sent to chase Bigfoot instead of the Yeti.
The seed for the herder's brother is already in the jeep when you drive to the chicken farm (right hand star) in Puerto Rico.
You have lantern and matches for the house. Go up in the attic because you hear a bumping noise it turns out is a raccoon as you make your way down to the door the jersey devil appears. You follow it outside it has nest of eggs in the top of a tree use rope to climb up and bring one of the egg shells to the lab.