Well, listening to the solo, it sounds like it's alternate picking and slightly palm muted triplets. Make sure you get the triplet phrasing - that's what makes the passage. Practice slowly with a metronome.

One thing you can do to help you if you can't pick that fast, is use legato. To get the triplet sound while still using mostly legato, you must accent the first and fourth notes of the pattern . Pick the 1st note, pull off, hammer on, pick the 4th note, then pick the 5th lightly (since it's on another string) and pull off. That's kind of the cheater's way. I'd suggest just practicing your alternate picking until you can tackle this.