Okay, I was playing a game earlier and this came up. The bat cowl reads as such:
This character possesses "Batman Ally Team Ability Symbol". If the character already possesses "Batman Ally Team Ability Symbol" and is adjacent to a wall or square of higher elevated terrain, lines of fire drawn to it are blocked when it is not your turn.

Now does that mean even pulse wave can't do anything about it?

Under the current rules, if the character has lines of fire drawn to it blocked by the last part of the text, then the Pulse Wave will not affect that character. Pulse Wave only ignores hindering terrain and characters when drawing lines of fire.

Under the 2013 rules, the character will once again be affected by the Pulse Wave, as Pulse Wave is going back to a wording that says "these lines of fire ignore all game effects except for walls, blocking and elevated terrain."

Thanks. Yeah so for three weeks or so that damn cowl is gonna be a pain in the butt to shoot Batman TA people with.

Under current PAC the Cowl will stop pulse wave. This is since pulse wave must first be able to draw a LoF before it starts ignoring.

However in the 2013 PAC PW ignores almost everything while drawing LoF. So then the cowl wouldn't do anything to protect the wearer.

Edit:to sloooooooow...