lol I am interested to see whether you get a serious attempt to tackle this one. I feel like it's just not a song that lends itself well to theory analysis at all, but I would love to be proven wrong.

Here's a shot from a music-theory hack:

Master of Puppets is a heavily-chromatic piece of music that starts out in a key that is perhaps best described as "open E", meaning it plays all the notes, alternating with the open low E string of the guitar. While it employs heavy chromaticism throughout, E is clearly the tonic. You could maybe say the feel starts out sort of minor blues, then sort of phrygian, then sort of locrian, but really it is authentically chromatic, and the "out" notes/chords are not really secondary dominants nor borrowed so much as just hammering on every half-step along the way. The chords are all root-five "power chords", of course.

It then modulates to doing the same thing in F sharp for a bit, then for the chorus it's back to "E Phrygian Blues" (yes I just made that up).

I can't remember the bridge or the harmony guitar breakdown.