The book “The Art of James Hetfield” has the chapter “Picking Techniques” which says:
Don’t expect to be able to play at extreme tempos right away; that would be like a neophyte jogger trying to run a marathon. Work diligently, every day, and increase your tempos gradually and comfortably. There are two basic rules for achieving great speed with accuracy: use subtle and short movements of the pick, and keep your arm relaxed and in a comfortable position. Any tension in your hand or arm will ultimately hold you back from playing accurately at fast tempos. Remember that Hetfield uses downstrokes whenever possible; only at the fastest tempos will he use alternate picking.
Play this simple quarter-note exercise with successive downstrokes. Start at a comfortable tempo, perhaps 120, and work up to 208.
The eighth-note exercise can be played with successive downstrokes at slow to moderately fast tempos, but will require alternate picking once the tempo approaches the 200 mark. Start at 80 and work up to 208.
A metronome is a must-have for any musician. It will come in quite handy when practicing these exercises, and for benchmarking your progress as you increase your speed.
If you are currently without a metronome, you can use this sampling of Metallica songs and their opening tempos as a guide: