RuneScape: Dragonwilds features various side quests that share similar names with those in the MMORPGs it’s based on, and Goblin Diplomacy is one of them. Here, it’ll have you running around with just a handful of vague clues in mind, so here are the exact things you need to do to complete it!
This is a quick guide that will skip the vague stuff to avoid confusion, because it’s entirely possible to start this quest by accidentally “completing” one of the steps.
Starting the Quest
There are at least three different ways you can start Goblin Diplomacy, but the “intended” way from what I can tell is to find and talk to Zanik. She can be found northeast of Bramblemead Valley, just before one of the paths leading down to the Whispering Swamp.
She’ll tell you about a prophecy that you need to stop, and to do this, you need to find a pair of amulets. The next two sections will show you exactly where to find both objectives. If you started the quest by stumbling into one of them, then feel free to skip to the relevant part.

Finding Bandosian Amulet #1 – Reliquaries
Okay, so the thing with this quest is that there seems to be a bit of randomness involved. You can find one of the amulets in either of the ruins that Zanik asks you to investigate, and it’s not always the same for everyone.
Normally, you would interrogate a caged goblin in both of these locations, and they’ll tell you about a chest hidden nearby. We’re gonna skip that because they’ll ask you for a specific food item before revealing what they know.
Here’s a map showing where both chests can be found:

One of these chests will always contain a Bandosian Amulet, while the other will be empty. For the empty chest, the hint is that it was already opened by something that left behind traces of mud and water.
Finding Bandosian Amulet #2 – The Garou Druid
The second amulet will require you to fight a level 3 enemy who uses poison magic, so make sure to bring your best gear and consider slotting in Tempest Shield to your spell wheel. Bring a torch or have Fire Spirit ready too, cause it’ll be dark there.
Now, head to the cave at the western part of the Whispering Swamp (map below). Before you go inside, cast whatever combat buffs you have and activate your light source of choice.
Here, you’ll find a Garou Druid who has slow poisoning attacks that can easily be dodged or blocked. Once you kill it, you’ll receive the Druid’s Bandosian Amulet, which is what you need for the quest!

Wrapping Up
Once you have both amulets, return to Zanik to hand them over. She’ll handle all of that prophecy mumbo jumbo on her own, and in exchange for your help, you’re rewarded with a new goblin-themed cape.
Quest completed, congratulations! If you haven’t done the Highlighting the Problem side quest yet, consider doing that next to unlock a crafting recipe for much later in the game!
Silly side note: I started this quest by stumbling into the Garou Druid’s cave and inadvertently completing that step. He actually respawns (that’s how I got the screenshot above) and can drop an extra amulet, which serves literally no purpose at all lol.