After you first examine the muddy lump, you are asked to kill 5 fetid blightrats in Rivervale and collect their claws. This is an auto updating step, but you will not get an update every time you kill a blightrat.
Examine the muddy lump again. You are asked to kill Nightblood Shadowgores until you can find a gem to make the pendant shiny again. This is another auto updating step. The best place to find the shadowgores is around the granary in Rivervale (just north of the bridge with the attached mill, in the cove west of where the Overfiend spawns). There is a single double arrow up Shadowgore standing next to the Granary, and there are 2 sets of Shadowgore (^^) and Harrower (^) packs within viewable distance from the granary (one near the bridge with the mill, and one around the corner toward the Overfiend).
After getting your update, you are asked to run to the Granary ( -539, -8, -343 ) in hopes of letting the pendant absorb some starlight and regain it's glow. You should be very close to the Granary already, so simply walk near the front door to get the auto update.
After this, you need to examine the muddy lump one last time to receive your Starshine Pendant.