a few tips:
Hand muting is important. *Both with your fret hand and tapping hand, you should be constantly keeping the other strings silent as you work your way from the G to the B and finally the e string.
Lots of gain and compression. *Vai was using a
Bogner Ecstacy at the time. *Bogners are known for their gain.
Practice. *I posted a lesson on that tapping a while ago here in the Lessons area. *Look it up and practice along with the .wav file included there. It's been a few months since that was posted. *I was about 85% fluent then. *I can play it near perfect now. *