Bud and Lou

"Recognize Joker's pets? Me too. That's why I had them shot and stuffed!"

- Penguin Bud and Lou were the Joker's two pet hyenas, but the Penguin has killed them and put on display in his Museum.

Between Arkham Origins and Arkham Asylum Incident
Sometime after the events of Christmas Eve but before Arkham Asylum, Joker got Harley Quinn two pet hyenas and named them Bud and Lou.

After Arkham Asylum Incident
After the Arkham Asylum Incident, Penguin had the hyenas shot and stuffed, then proceeded to put the pair on display in his Museum.

Arkham City Incident
Bud and Lou are on display in Cyrus Pinkney's Institute of Natural History, which has become the Penguin's stronghold in Arkham City.

When activating the display, the Penguin's recording says '"Recognize Joker's pets? Me too. That's why I had them shot and stuffed!" Scanning the hyenas solves the riddle "Have Joker's pets laughed themselves to death, or just eaten too much?"

Arkham Underworld Incident
Bud and Lou can be attained through upgrading Harley Quinn, and are used to fight beside her in combat.

Trivia

 * Bud and Lou were named after the renowned Comedic Duo - Bud Abbott and Lou Costello.
 * Bud and Lou were featured as Harley's pets or "babies" in Batman: The Animated Series.