During missions, NPCs can spawn. However, if I cannot battle ONE NPC first, how am I supposed to get the NPC to spawn during the missions.
Example:
I want to do mission The Drannik Extinction, but I cannot get a Drannik Archivist. How do I get an archive chip?

They drop from the NPC spawned by the mission. Until you find them, you can't get their drops.

Kill an NPC and another will replace it. Or wait the 8 hours and refresh your BT for more NPC's. You won't have a problem with enough Drannik Archivists, there are pretty common.

But how do I start the mission if the NPC only spawns DURING the mission?

You work your way up to the mission normally. Once you are on that part of the mission, that NPC begins to spawn, and you use the drops from it to complete that section of the mission chain. You don't need the drops to unlock it, just to complete it.

But I still need a Drannik Archive Chip to even START it, but the NPC only spawns after you start the missions...Or will it spawn as soon as you unlock the mission?

O.o I just answered that lol, they spawn once you are on that part of the mission chain.

But it's the first mission in the chain

Good God... Just NPC more and find them lol

Lol, sounds good to me. Thanks