Leo Dorfman, Neal Adams and Dick Giordano combine on World’s Finest 175 (May 1968) to introduce the Batman Revenge Squad.
The Batman Revenge Squad is made up of bitten ex-felons, all of whom were captured at one time by Batman. They choose to dress up in costumes that resemble that of Batman, and chant about how much they want to kill him.
Appropriately, they meet the Superman Revenge Squad, who do much the same thing, but with Superman. It just so happens that Superman and Batman are about to compete against each other in an annual competition, and the teams agree to work together to kill whichever hero wins.
The tests the heroes give each other are largely mental, but with some bizarre components to them. For example, Batman’s test involves Superman detonating a nuclear warhead. Just for fun. Cause nothing bad comes from setting off nukes.
At any rate, the heroes figure out that the Revenge Squads have planted bombs in the trophies, and defuse them before rounding up the bad guys.
Though the Superman Revenge Squad return within the year in Action Comics, this is the only appearance of the Batman variant.