Vatos isn't one of Samothraki's easy-to-reach beaches. Quite the contrary! It's in an inaccessible area of the island, beyond the mountains and far from any roads.
Vatos Beach is in the south, a few coves away from Pachia Ammos as you go eastwards. The homonymous river flows into the sea here through a picturesque canyon. Vatos is a wild sandy beach, with clear blue waters and strange rocky formations.
The easy way to reach Vatos is to go by boat. The alternative is to follow the mountain trails. One path starts from Pachia Ammos and cuts through steep cliffs that plunge into the waters below. It's not a long hike - about an hour - but it has some difficult and outright dangerous segments. Mountain climbing experience and not being afraid of heights certainly do help.
Another path starts from the church of Panagia Krimniotissa. If you follow it you can get to a height that overlooks the river valley. From there you can try to make your way down the steep hill, but there's no visible path. You have to go by feel alone.