I am currently having a debate over the Batman Cowl. Simply put, is line of fire blocked when you are higher up than the character trying to target you or is line of fire blocked when you are next to higher terrain on the lower rim of it?

This character possesses "Classic Batman Ally Team Ability Symbol". If the character already possesses "Classic 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.

The character it is attached to needs to be adjacent to higher elevation then the character it occupies.

Assuming the text in the units section is correct:
See bolded.