I used to boil/simmer skulls on my deer. Then a visiting PH from Namibia told me to just set the skull in a bucket of water outside for a few weeks. He was right, you get critters growing in that water that eat the skull clean. I don’t even skin them. Follow that up with a pressure wash and a peroxide soak exactly as Red Leg described and you’re done.
As an aside, we clean bear skulls by hanging them off our boat in a basket in AK. It is amazing how quickly the little critters in the ocean will clean a bear skull.
That works fine until your neighbor starts to complain about the smell that is coming from your shed.
If you live in a area that has red ants you can also build a cage to place the skull into to keep the other furry creatures from packing it off and placing the skull on the ant bed with the cage over it.