Hi DoomFan!
You are on the right track with this lesson, but it needs more days of practice to adjust your alternate picking technique at this tempo. It's difficult to note the dynamics of your take because of the mix issue, but I can notice that your picking is a bit weak and irregular yet, in both the palm muted sections and the parts without palm muting. This definitely need to be worked.
There are also some parts where some notes are missed, like the little section at 00:32. This means that there are some parts that need to be isolated and practiced as a loop, to be able to play it more precise, and to make your alternate picking more precise and off course, to improve the way you manage dynamics.
It would be also very good if you can make your guitar sound louder in the mix on the next takes.
Keep on the hard work!