[OP03-041_p1] - Usopp (Pillars of Strength: Alternate Art)

Does this "When this Character's attack deals damage to your opponent's Life" effect activate before a [Trigger] resulting from that damage?

First, your opponent checks their Life in accordance with the damage dealt, and then this "When this Character's attack deals damage to your opponent's Life" effect activates. After that, if the checked Life card has a [Trigger], your opponent can choose to activate it.