I - Rules
(see JITD, p. 22; FAQ, p. 2)
Attacks with the Breath ability use the Breath template to determine which spaces they affect. The template is placed against one side of the attacking figure (see diagram) and all figures underneath the template (friendly and enemy) are affected by the attack.
A Breath attack ignores rolled range, only missing on a miss result. If the attack does not miss, it deals full damage to each figure affected by it.
If a Breath attack is dodged by more than one figure, only one re-roll may be made (the first dodging player to the attacking player's left decides which dice, if any, are to be re-rolled).
The flame from a Breath attack billows out and around obstacles. It usually affects all figures under the breath template, but the flame can be blocked by walls and closed doors. Essentially, if a small flying figure could trace a legal movement path from the square where the Breath attack starts to the target - while staying within the breath template - then the target is affected. See the diagram on page 3 of the FAQ for examples. Breath attacks cannot be made through staircases.
II - Reference
Heroes with the Breath ability: none.
Items granting the Breath ability: Cone of Fire, Screaming Eagle Staff.