If I have Move Fiora Peerless to attack a battlefield with only one enemy unit, can I use Punch First during the showdown and get +10 instead of +5 might?

No, you cannot get +10 Might from Punch First in this scenario. You will only get the +5 Might from the spell.

According to the rules and the specific interaction with Fiora, Peerless, here is the sequence of events:

1. Initial Chain: When you move Fiora, Peerless to attack the battlefield, her "When I attack" triggered ability is placed on the Initial Chain because the battlefield is one-on-one.
2. Closed State: The game enters a Closed State because a chain exists.
3. Reaction Window: You can only play cards with the [Reaction] keyword while the chain is closed. Punch First is an [Action] spell, so it cannot be played while Fiora's trigger is on the chain.
4. Resolution: Fiora's trigger resolves, doubling her Might from 3 to 6.
5. Open State: Once the chain empties, the state becomes Open. You now have Focus and can play Punch First as an [Action].
6. Final Might: Punch First resolves, giving Fiora +5 Might. Her total Might for the combat becomes 11 (6 base doubled + 5 from the spell).

Why you cannot get +10:

• Timing: You cannot play Punch First before Fiora's trigger resolves because Punch First is an [Action], not a [Reaction].
• Effect Order: Even if you could play it before, Fiora's ability doubles her current Might. If you played Punch First first, she would have 8 Might (3 base + 5 from spell), and her trigger would double that to 16. However, because you must wait for the chain to empty to play an [Action], you are forced to resolve the trigger first, meaning the doubling only applies to her base Might of 3.

This is consistent with RiftJudge FAQ #8421, which explicitly states that you cannot play Punch First before Fiora's Might-doubling trigger resolves.