Here are the Codex - Bestiary entries for Nar Shaddaa, a bit skinny and underwhelming despite a vibrant planet of activity!
Go to the "Network district" and take the quest "[Heroic 4] Hunger of Vrblthers". Then enter the quest area and kill a "Aged vrblther" (Champion level 22)
Codex entryHailing from the planet Varl, vrblthers are common pets among the wealthy and powerful Hutts. When Varl was exterminated ten thousand years ago, these valiant bipedal predators owed their survival to their owners who took them with them to Nar Shaddaa and Hutta.
Unaffected by pollutants and other toxic products that saturate their new environments, these creatures quickly saw their numbers increase. Packs of vrblthers can now be found on the lower levels of Nar Shaddaa, constantly looking for their next meal.
Empire : Kill the "Killer Gundark" (elite level 10) on Dromund kaas
Republic : Currently it is not indicated anywhere how to get this entry, the only referenced Gundark I have found is in a Smuggler quest but obviously does not grant entry either.