Some pics of my finished pig puppet.
He's mostly sculpted polyfoam, synthetic fabric, nylon webbing (backpack straps) and contact cement, with lots of machine and hand stitching. He's also equipped with removable rods in the forelegs. He has fabric lining inside the head so that the puppeteer's hand doesn't feel uncomfortable on the foam, which overtime gets nasty and textured when it's not covered.
His hooves and snout are paper mache, for the nice definition and strength they need to have.
He can be operated on two or four legs.
The trick to his stability and versatility is that the axles for his legs are stiff, made with rods going through the legs and body. To prevent tearing, each hole is lined by a piece of PVC tubing that is slightly bigger than the axle. That bulge in the neck is avoidable and doesn't always show. Next puppet I build this way will have an extra step top prevent that altogether.
The finish on him is to work with the story that he was badly prepared and cooked all wrong by an inexperienced cook. I made this texture by choosing a textured polar fleece, and by rubbing some very diluted acrylic paint with a rag, while the puppet was moist. It prevents stiffening of the fabric, and prevents brush marks, acting more like a dye.
He now lives and performs in Spain.