If I move Sett into a battlefield to start a showdown, then during the showdown I play Zenith Blade to move Leona (Determined) to that battlefield, does Leona's 'When I attack' trigger activate, or did she need to be present when the showdown started?

Yes, Leona's 'When I attack' trigger will activate. Leona does not need to be present when the Showdown starts.If a Unit controlled by the Attacker becomes present at the battlefield after Combat begins, it will gain the Attacker designation during the Cleanup phase following the action that caused it to become present. The sequence works as follows: (1) Showdown begins when Sett moves to the battlefield, (2) Focus passes and you play Zenith Blade during the Showdown, (3) Zenith Blade resolves and moves Leona to the battlefield, (4) During Cleanup after Zenith Blade resolves, Leona gains the Attacker designation because she's now present at the battlefield where Combat is staged and her controller has the Attacker designation, (5) Leona's triggered ability triggers when she gains the Attacker designation and is added to the chain as a Pending Item. The 'When I attack' condition is met when a unit gains the Attacker designation, which happens during Cleanup after Leona arrives, so her ability triggers before Combat Damage resolves.