Play scales to practice your alternate picking. Most of the song is picked at an exceptionally fast pace, and it would be very difficult to accomplish using all down-strokes. Practice picking down and then up alternatively to get the most out of your picking hand movements.
Set a metronome at a comfortable pace when you start practicing and then increase the speed as your picking hand gets quicker.
Play a scale, but skip the notes on every other string. Gilbert uses the D Major Triad and the D# Diminished Triad in the song, so practice ascending and descending runs in these scales with skipped strings.
Play a note on each string, working sequentially downwards, and then do the same on the way up. This method is called sweep picking and it's used in "Scarified." (see Resources for exercises).
Play the major sixth and diminished seventh patterns that make up the final arpeggios in "Scarified." The patterns are moved onto different frets throughout the song, but if you focus on the shapes, you will be able to apply them across the fret-board in the same way you can with a scale.
Combine these techniques to play the song.