You have to some work on kp-shadowsquirrel's 3D models before printing.
On the .obj file, the different parts (body, mane, tail...) are separated, you have to assemble them in an unique watertight 3D model (I use the union boolean modifier in Blender) then you can convert it to .stl and print.
You also need to increase the number of polygons on each part before joining them to have a good result (subdivision surface in Blender).