One thing I've noticed is that they seem to be fairly weak at close range, as long as you don't go all the way into melee. At this range, she won't charge around or fire her projectile attack. Instead, she will just walk slowly towards you and occasionally use her area blast.

The strategy I've been using so far with my Vanguard on Insanity is to first try to isolate the Banshee, and then keep doing Charge, quickly step back out of melee range to avoid her instant kill attack, then keep shooting from close range until Charge is ready again.

While it's fairly easy to see when she's about to do her area blast, I usually ignore it. It has so far only done enough damage to drop my barrier, which I can quickly get back up again with another Charge.