"Intense", "frightening" and "overwhelming" are all defining "beautiful." In effect, the phrase "in a/an...way" is making those adjectives function as if they were adverbs. You could reconstruct it as "extraordinarily but intensely, frighteningly, and overwhelmingly beautiful." She thought that her beauty was cold and intimidating in some way.

When something “overwhelms” you, it means that its effect on you is so intense that you cannot handle it, or process it, or understand it in a normal way. It is simply too much.