Source: World's Finest Comics #111 (1960)
Type: The real deal (since retconned)
It begins when socialite Bruce Wayne and his ward Dick Grayson catch a news report that announces, pretty much in the same breath, that Superman and Clark Kent have gone missing. Before the media can clue in that the two are one and the same, Batman and Robin spring into action find Superman. They have something to go one, because Supes told them he was on the trail on racketeer Floyd Frisby who was hiding in the "general area" of a very specific, small fising village in South America. That was a week ago, and here's what actually happened:
Batman and Robin follow that trail, fight some marauding beasts for good measure, and are then jumped by what appear to be ancient Mayan soldiers. They let themselves be captured and led to a hidden valley with one of those ancient kingdoms protected from History we're always hearing about. Their king, as you've no doubt guessed by now, is Superman. An amnesiac Superman tapping into his aristocratic Kryptonian side, no doubt. He notices their strange costumes, but doesn't clue into the fact that they're a derivation on his own. Brain damage, I guess. Batman and Robin are welcomed as guests, and later get a guided tour of the frescos painted that week to celebrate the new god-king's arrival.