Since the character can't move to avoid a blow while climbing, enemies can attack the character as if the character were
stunned: An attacker gets a +2 bonus, and the character loses any Dexterity bonus to Armor Class.
Ack... looks like that duel last night will have to be retconned. The PC-duelist missed by 1 point when her opponent was climbing up a chain... Good thing we stopped right after the end of that fight.