Obtain the Bat, Wolf and Mist transformations.
These items allow you to transform into different forms, each with their own skill set. The Bat can fly and use radar to "see" in the dark, allowing you to easily access new areas. The Wolf can swim, which is key in exploring the entire map. The Mist transformation allows you to pass through fences and gates that you would not be able to in your normal form. These can all be found in the Normal Castle. You can get Soul of the Wolf and Form of Mist as soon as you work your way to their respective locations, but you must have the Mist Transformation before you can reach Soul of the Bat.
Use the map linked in Seeker to specifically locate these areas.
The Soul of Wolf is found at the top of the elevator in the Outer Wall. There is a switch at the very top of the wall, above the elevator, that unlocks the elevator gate when you flip it by walking past it.
The Form of Mist is found in the Colosseum. After the Minotaur boss battle, go into the room directly to the right.
The Soul of Bat is found in the Library. Go into the largest room and take the middle door on the left. You will find yourself in a save room. Again take the door on the left and follow the path down and to the left, using the Mist transformation to get through the grate.