Double-pick the whole thing. Try up-picking the first note (0) then down-picking the 4 as it's on the beat. Then up on 0 then down on 7 and so on. So what you're effectively doing is down-picking all the notes when your fingers are on the strings, and up-picking all the open notes. Do this through all measures. Practice slowly at first. ALWAYS strive for accuracy...then speed.

The double-picking technique is what Dick Dale uses to play Miserlou, a 60's surfer song made popular in the movie Pulp Fiction. As an aside, Miserlou is an old, old traditional Greek folk song and a line-dance. I first started to play Miserlou when Dick Dale released it. (I guess I've been around a while. So has Dick.) By the way, Miserlou is about twice as fast. After you master Thunderstruck, try Miserlou, if for nothing else than a great double-picking exercise. And if you ever get a gig at a Greek wedding, at least you'll know one song.

Or, you can play it without picking. Use mild distortion or any other means to get some sustain for the notes. Again, pluck the open string, but only the first open string to start the piece, then it's non-stop hammer-on and pull-off. It's good exercise and will ultimately sound better than picking it. Good luck.