Can a player reveal a hidden Tideturner from one battlefield and use its swap ability to swap with a unit at a different battlefield where a showdown is occurring?

Ruling: Yes, this is legal. You can play reactions from any battlefield when there is an item on the chain, regardless of where the showdown is occurring. Hidden restrictions only apply to targeting, and Tideturner has errata that allows its ability to bypass that restriction.

Nuances:

• You need something on the chain to react to, or a priority window to play Tideturner from hidden
• If the attacking unit has an attack trigger, you can respond to that
• Otherwise, you must wait until the opponent plays an action speed effect or passes focus and priority to you before you can play Tideturner