The Fossil Skull is one that you can find by exploring Pokémon Brilliant Diamond and Shining Pearl. You'll have to look for it in a specific place, but when you find it, you can bring an old Pokémon back to life and travel with one from the past. Here's where you can find the Fossil Skull in Pokémon Brilliant Diamond and Shining Pearl.
You can find the skull fossil when you have received an explorer kit. You will receive it when you reach Eevopolis and talk to the old man near the Pokémon Center. You can now visit the Grand Underground and explore the area to find the Skull Fossil.
You have to look for it by investigating the fossil excavation sites, the orange icons on your map. You can find them along the paths between the many biomes of the Grand Underground. The skull fossil is a difficult item to find, so we recommend that you use the Diglett and Dugtrio bonus you receive from finding these Pokémon in the paths to increase the chances of it appearing.
It is important to note that Skull Fossil is exclusive to the Pokémon Brilliant Diamond version. If you own Pokémon Shining Pearl, you will not be able to find this fossil. Instead, you can only find the Skull Armor. You will need to trade with someone who has a Pokémon Brilliant Diamond version to acquire Cranidos.