Can a Hidden Blade hidden at Battlefield A be used as a reaction to kill an attacker at Battlefield B?

Ruling: No. When you play a hidden card, if it targets, those targets must be chosen from among options at the battlefield where the card is hidden, unless the ability explicitly restricts targeting in a way that makes this impossible.

Nuances:

• This targeting restriction applies to all hidden cards, not just Hidden Blade
• Even though Hidden Blade's text says "target a unit at a battlefield" (not "THIS battlefield"), the Hidden mechanic adds the extra targeting restriction
• Some cards like Tideturner have errata that explicitly override this restriction