Hinata essentially makes you immune to taijutsu every 3 rounds, except the first tai, but what I count on fighting her is that people have her in spot 1 (the top right looking at it as if it were your team) so my GNW Kiba's tai gets through. Then I base my combos off of his tai. This gets under the shield a little so it's easier next round.
In general Hinata can be taken down during her "invincible rounds" with mysteries and debuffs (can't confirm but does Sleep cancel out her shield? But I do know that damage can be done with poison/ignite) and other ninja like my strategy with the 1st tai or someone like Kankuro. (If his puppet is around it goes right through.)
Again, can't confirm, but Hinata's shieldy-thing seems to cancel out whatever taijutsu *ion group skills you have (like it doesn't seem to make a difference); you just have to work around the mystery.