The river of lava we are out for is part of the island’s northernmost lava formation. Even during the day, this area is dark. This comes as a plus when you’re searching for skyshards.
Head south from the northernmost area of interest. Soon enough, you’ll spot the river of lava and a couple of small islands on it. One of them is home to the skyshard. But try not to show your enthusiasm by jumping into the lava and swimming toward the main rock. I can confirm, thanks to events that transpired only to prove this point, that it will most likely cause death. Although it doesn’t look like it, I’ve been able to climb this rock on one side only – the west. Be sure not to repeat my mistake, and save one soul gem.