This is an Ancient Wardstones quest.
This seems like an impossible chore, but you have the Magitech Fire Blaster! Smack a Ripening Cocoon and dozens of Sicklefang Spiderlings will boil out. Burn them all, then finish the cocoon. Rinse, repeat. Do NOT kill the Broodmother until you have finished all the cocoons and spiderlings, or put the Fire Blaster on your hotbar directly, else the last cocoon you pop may spawn spiderlings and overwhelm you when the flamethrower vanishes from your quest tracker!
Then kill a Sicklefang Broodmother. She is not so bad if you do not have to fight 300 Spiderlings at the same time.