Original guide: Guide to getting Panda and Chicken outfits by globalastroIn Alker Harbor, you will find Bamboo Stalks (named Bambusoideae in SG Luna, I believe) and Old Wood Signs. These are the only attackable items in the town, and each hit does 1 damage to it. Granted it takes a little while to "kill" these items, There is a somewhat low chance of receiving parts of these animal costumes.
The chicken outfit pieces are dropped by the Old Signs.
Panda outfit is dropped from the Bamboo!
(Thanks to cinderboy for the nice images)
The easiest way to kill these items is with a Rogue with their fast attacks or with DoT attack from magic users, no matter what attack you use, each hit does 1 damage. The DoT skills help because you can cast something like Envenom AND Fireball on them if you are a wizard, doing 1 damage per hit of the DoT attack if it takes, and attack at the same time.