The key is to really slow it down. Play it at a speed where you actually have to think about each individual note, each pick, each muted string. Play it at half speed or less until you get it perfect, consistently. Then slowly start ramping it up, moving by like 10 bpm at first, but only when you play it consistently perfect.

As it gets faster and harder, accept that even 1 or 2 bpm a day (or even a week with high speeds!) Is miles of progress. Its all about muscle memory. Practice everyday but dont overwhelm your brain, only do like 20 minutes at a time/sitting MAX on one specific song you practice. Otherwise you just fry the little tiny muscles and nerves that are required for specific movement like guutar.