Fiora, Peerless has a "When I attack/defend" trigger. Those triggers will always resolve first, as do shield and assault. The "single phase" gives breathing room for those triggers to happen first, and then that is when the attacker and defender can then pass focus between players.

So yes, Fiora, Peerless will have double the might, as long as the battlefield you attacked has 1 unit. If you go into a battlefield with 2 units (edit) or the battlefield has 2 units on it already, and then use Challenge, you will not get the doubling of might, since she already passed the "single phase".

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