My opponent plays Elder Dragon while I have one unit at each battlefield (I hold both battlefields). Can I play a Hidden Tide Turner on one battlefield in response to this? How does this interaction resolve? Does my opponent have to declare the targets for Elder Dragon first before I react with my Hidden Tide Turner?

Yes, you can respond to Elder Dragon’s play effect by playing a hidden Tideturner as a Reaction.

Declarations and Priority

Your opponent must declare their targets for Elder Dragon's ability when they play the card. According to the game rules, Elder Dragon's "When you play me" ability is a triggered ability that uses the chain. When the opponent plays Elder Dragon, they must choose their targets (up to one enemy unit at each location) and place the effect on the chain.

Once they have declared targets and added the effect to the chain, you gain priority, at which point you may play your hidden Tideturner as a Reaction.

How the Interaction Resolves

Because your Tideturner is a Reaction, it will be added to the chain on top of Elder Dragon’s triggered ability.

1. Chain State: The chain currently consists of (bottom) Elder Dragon's ability, (top) Tideturner's playing/triggered ability.
2. Resolution order (LIFO - Last In, First Out):
   • Tideturner resolves first: You move Tideturner to the location of your other unit, and that unit moves to Tideturner's original location.
   • Elder Dragon's ability resolves next: It re-checks the status of its targets. As clarified in RiftJudge FAQ #9919 and #9968, because the units targeted by Elder Dragon have moved to different locations (or are no longer at the locations where they were originally targeted), they no longer fulfill the targeting criteria for Elder Dragon’s effect. Consequently, they are unaffected by the 1 damage.

Summary

• Targets: Your opponent declares them first.
• Reaction: You can react once the ability is on the chain.
• Result: By swapping your units, you move them out of the positions Elder Dragon is targeting, causing those targets to become "invalid" or miss their requirement (as per Rule 359.3.e.9), effectively saving them from the damage.