Can I use fiora worthy ability in an active showdown

Yes — but only if its trigger condition happens during that showdown.

Fiora, Worthy's "When a unit you control becomes [Mighty], you may pay [C] to ready it" is a triggered ability, not an activated one, so it isn't blocked by the rule that keeps regular activated abilities out of showdowns (Rule 145.2, 381). When a unit you control actually becomes Mighty (hits 5+ Might, including from a mid-showdown buff or a defender's +1), the ability goes on the chain and can be responded to; the [C] is paid as it resolves, and the ready happens then. If nobody became Mighty — for example Fiora was already Mighty before the showdown started — there's no trigger to use.

See FAQ 6927 for the same sequence: a unit becomes Mighty mid-showdown, Fiora's ability is used, cost paid, unit readied.