Can you play Rengar Ambush as a reaction to a different battlefield from a spell that targets your unit in a different battlefield?

Yes, you can play Rengar, Trophy Hunter as a reaction to a spell that targets your unit at a different battlefield, provided you meet the conditions of his ability.

The Reasoning

1. Reaction Timing: A spell targeting your unit at a battlefield goes on the chain, creating a Closed State. This grants both players the timing permission to play [Reaction] cards (Rule 813.1.c).
2. Ambush/Reaction Permission: Rengar, Trophy Hunter’s ability grants the permission to play him as a [Reaction] to any battlefield with enemy units, effectively bypassing the standard requirement to have units present or control the battlefield.
3. Legality: Because the state is Closed, you are legally permitted to play a card with [Reaction] timing. Rengar’s specific ability allows him to be played to a battlefield with enemy units, making him a legal play in this situation.

The Sequence

1. Opponent plays a spell: The spell targets your unit at Battlefield A and goes on the chain. The game enters a Closed State.
2. You play Rengar: Because the game is in a Closed State, you have [Reaction] timing. You play Rengar, Trophy Hunter to Battlefield B (assuming Battlefield B has enemy units).
3. Chain Resolution: The chain resolves in Last-In, First-Out (LIFO) order.
   • Rengar, Trophy Hunter enters Battlefield B first.
   • The opponent's spell then resolves, targeting your unit at Battlefield A.

Important Note on Targeting: If your opponent’s spell targets a unit, Rengar’s entry does not interfere with the spell's targeting relationship. Per Rule 359.3.e.3, targeting relationships are maintained as long as the targeted unit remains on the board, even if Rengar enters play elsewhere.

Note: I could not fully verify this ruling against the retrieved rules.