If my opponent attacks with Fiora Peerless onto a battlefield, where I have a Pouty Poro, do I have a chance to gust her to hand before her might doubles?

Yes, you have a chance to play Gust to return Fiora, Peerless to your opponent's hand before her Might doubles.

Here is the timing sequence based on the Showdown flow:

1. Initial Chain: When Fiora is designated as an attacker and moves to the battlefield, her "When I attack" triggered ability is placed on the Initial Chain.
2. Closed State: The game enters a Closed State because a chain exists.
3. Reaction: Because Gust has the [Reaction] keyword, you can play it in response to Fiora's triggered ability while the chain is still closed.
4. Resolution:
   • You play Gust, targeting Fiora. (Note: Because Fiora has 3 Might, she is a valid target for Gust).
   • If your opponent does not have a way to stop Gust, it resolves first (LIFO - Last In, First Out), returning Fiora to their hand.
   • After Gust resolves, Fiora's triggered ability attempts to resolve. Since Fiora is no longer at the battlefield, the ability will fail to find its target/source and will not double her Might.

Important Note: Because Fiora's ability is a "When" trigger, it is evaluated at the moment of designation. As long as the combat is one-on-one at that moment, the trigger successfully goes on the chain. However, by using a [Reaction] spell like Gust to remove her from the battlefield before the trigger resolves, you prevent the effect from successfully applying to her.