Can you cast a spell with an action that targets a different battlefield while you are in a showdown?

Ruling: Yes, there is no restriction on targeting during a showdown. You can cast spells targeting different battlefields while in a showdown.

Nuances:

• Hidden cards are an exception - they need to target units at the battlefield where they were hidden
• If a card instructs you to target a unit at "a battlefield," the target remains legal even if the unit moves to a different battlefield before resolution (unless the card was played from hidden, which adds a "here" restriction)