The Loud Bird bonus round rule is one of the many rules that can be applied during the Bonus Round episodes. It is offered when entering floors 3, 4 or 5 with any character (more common on floor 4), but it is rarer than the other rules, appearing only a third as often as other rules.
When the rule activates, only the enemy in each fight will gain a permanent innate Dodge every turn, meaning that the first attack every turn will be dodged. Since this prevents the first instance of damage from being done, which can cause troubles for most characters, this rule is rarer.