If I attack with a Bird token unit, can I play the Stalking Wolf to that battlefield if that's the unit I target to kill with its ability?

Based on the most current RiftJudge FAQ and the core rules for the Ambush keyword, no, this is not legal if the Bird token is your only unit attacking that battlefield.

Here is the step-by-step breakdown of why this doesn't work:

1. Location Control: When you are attacking a battlefield, you do not control that location (your opponent does). Normally, you cannot play units to a battlefield you don't control.
2. The Ambush Requirement: Your only permission to play a unit to an enemy-controlled battlefield comes from the Ambush keyword, which requires you to have a friendly unit present at that location.
3. Paying the Cost: As you initiate playing Stalking Wolf, you must pay its additional cost by killing the Bird token.
4. Invalidating Ambush: According to Rule 822.3, "If there are no units at the location chosen before Finalization completes for any reason, then it is no longer a valid location by Ambush’s reasoning and cannot be played there." Because the Bird token is dead, your Ambush permission vanishes before the card finalizes.

Even though Stalking Wolf's card text says "You may play me to its battlefield (even if you don't have other units there)," this specific wording does not override the fundamental rule restricting you from playing units to an uncontrolled enemy battlefield without a valid Ambush permission.

What you can do instead:

• You can still kill the attacking Bird token to pay the cost, but you must choose to play Stalking Wolf to a different legal location (such as your base, or another battlefield where you control units).
• If you had another attacking unit at that battlefield alongside the Bird token, you could kill the Bird token and play Stalking Wolf to that battlefield, because your other unit would keep the Ambush condition satisfied.