I have tested this some time ago in MM, and this is what I found:
If you press Up, Link walks right 'into the screen', directly forward. The camera moves with him, so the distance fom camera to Link is always the same.
If you press Down, Link walks right 'to you', so exactly the opposite direction. The camera moves with him again, to keep the distance the same.
If you press Right or Left, he moves right or left and the Camera stays in the same position, but rotates, so that Link is always in the middle of the screen. Maybe then it moves a little bit forward or backward to keep the distance the same.
So if only left/right was pressed, Link would run in circles.
If I programmed it I would do it this way:
The angle the camera has now is treated as forwards, +90° is left (or right, I don't know), +180° is backwards, and +270° is right (or left).
Then the Control Stick input returns a direction and a speed of movement.
Link is moved in the direction the Control Stick returns + the angle the camera has right now.
The higher the speed, the more he moves in this direction, and also the animation he has is set according to the speed.
Then the camera rotates, so that Link is in the middle of the screen, and then the camera is moved forwards or backwards, so that the distance to Link is always the same.
How the camera reacts to Links movement Up or Down I don't know, but I would do it like this:
If Link's height is changed the camera's up/down angle changes, so that he is always in the middle of the screen, but this angle has only a certain range in which it can move, like +45°/-45° from the default position. If the angle value would be more/less than that, then the camera moves up or down.
And when Link is on solid ground then the camera is set to the default height.
Of course it's a little bit more complicated than that; in MM if Link has a very high speed he can't turn in just any direction in one frame, but has to slowly change his angle over several frames.
Also I don't know if you could do it like that, I never programmed in 3D, and sorry if I explained some obvious things, but maybe it's some help.