Instructions
Travel all the way through Katzenstein's Lab. Collect wooden planks as you go, which are scattered throughout the general area and lab. Face Dr. Katzenstein and go up the stairs to the left onto a terrace.
Use the wooden planks that you had previously gathered to build a wooden bridge from the terrace; go back and get more pieces of wood if you don't have enough to complete the bridge. Locate Smogger on the bottom-right corner of the map of Katzenstein's Lab inside the pavilion.
Defeat Smogger using your cards and various attacks; this may take a few tries. Collect the Green Fairy after you defeat Smogger and select her as your new pet.