Hi mate, great to see you working on this one!
I can say that you have most of the lesson mastered. You can play the riffs at tempo and the chord changes are sounding smooth and most of the time tight with the drums.
The main thing to improve on this one is the tone that you get, and this is not based only on your amp setting, I think that there is something happening when you play alternate picking with palm muting. In the first section, there is a high pitch harmonic that appears, in other parts the palm muted tone sound too raspy and the note is not sounding there. You should experiment with the position of your right hand palm, moving it and experimenting how the sound changes, and the same with the pick angle. The more you angle the pick, the less clear is the sound that you get, so there must be the main problem.
Besides this, I agree with Ben about the timing issues in the section that he marked. Take care of it.
Keep on the hard work!