House of Thule -> Conquest -> Exterminator
"This special challenge can be completed during the mission "Catastrophic Power"
[ ] Defeat all drachnids before confronting Al'Kabor.
Strat: Last time I did the Catastrophic Power mission which is an instance of Al'Kabor's Nightmare zone, there were 12 drachnids up, all of them on the final Dreadlands island, although two of them were out on the rocky edge of the island instead of near the pyramids. If you don't have a tracker, make sure you count all 12 drachnid kills before hailing Al'Kabor.
After hailing Al'Kabor, there are a few minutes of NPC shounting, then Al'Kabor turns into a skeleton and goes active -- the Exterminator achievement is granted at that moment for all players in the instance (unless your character achieved it already).