This quest is not available in game.
Defeat the Gorishi Hive Queen once she is summoned.
Bring the Gorishi Queen's Brain to Alchemist Pestlezugg in Gadgetzan.
- Gorishi Queen Lure (Provided)
Here's the lure. Inside the hive network should be a crystal of some sort. We think the silithid use the crystal as some sort of hive-wide attunement device. As for where this crystal might be, I'd say try the hatcheries inside the hive.
Using the lure on the crystal should roust out the queen, but be warned - she will probably be protected by several guards. Take out the queen and remove her brain. As icky as that sounds, we desperately need to study it. Good luck, <name>!