If I'm holding a zone and my opponent attacks and starts a showdown, and then I reveal a hidden card to win the showdown, do I get a conquer point?

Ruling: No, you do not get a conquer point. You only score a battlefield via conquering when you GAIN control of the battlefield, not when you successfully defend a battlefield you already control.

Nuances:

• Winning a showdown while already controlling a battlefield means you maintain control, but do not reconquer it for a point
• You can only score a point if you haven't already scored at that battlefield during that turn (either on your turn or your opponent's turn)
• The rule states that control is only established if you do not already control the battlefield