If you want to remove the fog from the map, you've come to the right place. This page of the Tower of Fantasy guide will tell you how to unlock the entire map.
The main storyline will lead you to different parts of the world. However, the fog will not disappear automatically. You have to take care of it yourself.
To unlock full visibility of a given region, you need to find Omnium Towers. Each sector has one. Even if the map is covered in fog, these towers are marked on it, so you will certainly not get lost.
Once you get on it, talk to the robot on each Omnium Tower. After that, you will discover the area. You have to do this every time you enter a new region.
It is worth noting that not all lands will be available to you from the very beginning. Some will only unlock once you develop the Suppressor. If its level is too low, you will start to lose health quickly if you venture where you shouldn't. You can read more about this device on a separate page - Suppressors.