The Bristlebacksquest will appear on your map when you arrive in Chainscape for the first time. Note that you would not be able to finish the quest until you are done with the fourth main story quest in the game.
Search West of the Quarry for Bristlebacks – Horizon Forbidden West
Nevertheless, it’s a lengthy one for a sidequest, and you can progress through it as you go along the story as well. The first step is to talk to Javad the Willing in a nearby Tavern. Follow the objective marker and travel to the quarry to examine the dead Bristleback.
Once you’re done, walk up the path and enter the mine. The quest markers will be your guide until you reach a collapsed trackway. Turn right when Aloy comments on this.
You know you’re going the correct way when you reach a room with two Bristlebacks. Defeat them and head into the tunnel on the right side of the room. Use the broken tracks to know if you’re going the right way!
Climb down a small room on your left, read the note that’s chilling with the blaze barrels.
Trace back your steps to exit the mine then go back to Jawad. This is the time when you need to put a hold on this quest and come back to it after finishing the main quest, The Embassy. After you finish, you’ll be given a quest to visit a rebel camp.
Make your way towards the Rebel Machine pens, use your Focus to spot the machines and rebels then defeat all of them. Afterwards, you will see a drawbridge just a few ways ahead. Shoot the ropes holding up the bridge and cross it to reach the cave on the other side.
A cutscene will play (no spoilers!), and then you’re free to go back to Javad. The quest completes after you finish speaking to him.
