The beginning can be done with just a swirly pick scrape (watch Vai - he's also using his other hand to mute and create different pitched overtones). Not sure what she's using, but you can do that without any gadgets.
@1:59, combo of pick scrapes and looong slides down the top strings. No need to go overhand, it's just flash...
The tapping part is definitely a big part technique, but you also need the right sound on your amp.
Personally, I never tap, I went through that stage and gave it up shortly afterward lol. It's cool, but just not my thing.
Look up some lessons on tapping, I'm sure they're all over youtube.
(you'll also notice that they are both playing with a good amount of delay on their guitars. WORL of difference when you're trying to get that BIG sound).
