A good beak is essential and I spent a fair amount of time on this.
First make a basic pattern, here it's expanded polystyrene foam. Like the "hat" I wrapped in cling-film then applied layers of PVA and paper, in stages with drying in between.
After I'd made the top-half the foam was trimmed smaller and the process repeated for the bottom half.
Notice how the end is rough and splayed-out, this helped with joining to the head-piece
Some bits of metal were added to form a hinge (cheap Meccano-a-like kit)