If Rengar Pouncing is my chosen champion, if my opponent starts a showdown at open battlefield, can I play Rengar as a reaction because it has reaction tag or am I confusing ambush?

No, you cannot play Rengar, Pouncing as a reaction to your opponent starting a showdown at an open battlefield.

1. Can you play him?

No. While the [Reaction] keyword grants you the timing permission to play a card during a Closed State, you must still satisfy the location requirements to play the unit. Per FAQ 8779, you may only play units to your base, a battlefield you control, or a battlefield you are attacking. An open battlefield is uncontrolled (Rule 344.2), and you do not gain control of a battlefield until you have legally played a unit there.

2. Ambush vs. Reaction

• [Reaction] provides the timing permission to play a card during a Closed State.
• Ambush provides additional location permissions, allowing you to play a unit to a battlefield where you already control other units.

Rengar does not have Ambush, and because you do not control the open battlefield, it is not a legal location for him. You cannot use the [Reaction] timing to bypass the requirement for location permission.

Summary of Timing and Designation

1. Opponent's Move: Your opponent moves to an open battlefield. It becomes Contested, and a showdown begins.
2. Your Response: Although the state is Closed (permitting [Reaction] timing), you must still target a legal location.
3. Legality: Because an open battlefield is uncontrolled, you have no legal location to play Rengar.

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