I have seen a bunch of guides advising people to not use the Wonder Weapon against these skulls, but it is by far the best method to use it against them. Don’t bother using your bullet weapons.
Every skull has a 50% damage cap threshold that will cause them to summon spikes around them, this means that you can never kill a skull in one go so don’t rush it.
One charged lantern shot is enough to immediately reach that threshold. This lantern is at PAP4, but I also tested it with PAP3.
TLDR: Throw a nade at the skulls mouth, follow up with a charged WW shot, avoid the frost explosion around it after. Repeat. Skull is gone.