To find the entrance of this public dungeon, you have to follow the river in this area. There is a bit of swimming needed as well, but don’t worry, you won’t freeze.
Unlike the “troubles” you have to go through in the other Wrothgar public dungeon shard hunt, it is not the case in this one. It is also not easy as well. At the beginning head toward the eastern part of the first room. There is a small passage, not shown on the map, you need to go through. It takes you to a new dungeon area. Now you have to progress a bit, just keep going, following the road, until it takes you past a small passage, just next to the waterfall. This is where the area is a bit wider. Follow the river and spot the second waterfall. On top of it, there is our 1/3 skill point. Go around the waterfall and climb it. There is a rather strange teleporting animation done from here, don’t know if it is intentional or it was a bug.
Sand Kingdom Moons - Super Mario Odyssey Power Moons