Vest: Cut a 12"x 30" rectangle from faux fur and fold in half; cut opening for head along center seam.
For monster legs, cut legs off tights, then cut each tight leg into two pieces. You will have eight pieces total: four footed pieces and four tube pieces. Set aside two of each type, which will become sleeves and long socks for baby. Stuff four remaining legs of tights with batting and hot-glue ends to seal.
Download and print the horn and claw templates at parents.com/baby-monster. Trace templates and cut eight claws from polar fleece. Hot-glue four of the claws to ends of stuffed tights legs.
Hot-glue two legs to each side of fur vest. Attach Velcro tabs between legs and on sides of vest to keep it closed.
Glue the tabs of the four additional claws together to wrap around baby's wrists and ankles. Baby should wear remaining striped footed tight pieces on legs and tube pieces on arms.
Cut four horn shapes from felt and hot-glue around edges to make a pocket. Cut two circles from faux fur. Stuff horns with batting and hot-glue to faux-fur circle cutouts; attach to hat with hot glue.