This quest is given by the Nomarch in the Final Dominion. Click on "Slay the Shadow Cat" to get the following information about the quest:
The bulbous merchant steps forward. "My explorers bring me terrifying tales of a evil monster lurking in the Western Jungle. They say it is a great cat made of shadowy darkness. It has already brutally murdered several of my servants. Kill this inconvenience and you will be compensated"
Go to the Western Jungle and adventure in "Enter the Western Jungle " until you encounter the Shadow Cat. It will be a tough fight! Once you have slain the Shadow Cat, go back to the Nomarch to claim your reward.
Upon reporting to the Nomarch in the Final Dominion you are rewarded with... [I currently haven't completed this quest so I don't know the rewards, please edit in the items (if any) and favour rewarded].