For this achievement you need to have discovered 30 seperate locations on your Solstheim map. An undiscovered location on your HUD radar will be a black image with a white outline. To discover it you need to walk up to it until you get an onscreen message saying for example, 'Brodir Grove Discovered', in large white writing. When a location is discovered, the image on your HUD radar will turn into a white image with a black outline.
You will travel to a minimum of 10 locations just doing the main quest, but travelling to your quest destinations will undoubtedly allow you to discover more locations.
You only need 30 locations and there are a total of 58 in Solstheim, so there are more than enough to obtain the achievement without much effort.