After the wholesale destruction in Metropolis, Bruce Wayne is convinced that Superman is a threat to the planet. So he starts figuring out everything he can. His entire arsenal - his intelligence, his gadgets, his detective skills - are bent to uncovering whatever he can.
He learns about Clark Kent, and about kryptonite. And he makes plans.
Meanwhile, Superman has figured out somebody is after him. His superhuman senses make this not necessarily easy, but possible. So he tracks down this looming Batman figure, with lead-lined armor, and fights him - only to find out it’s a robot. Bruce Wayne has been filming the entire encounter.
Wayne finds that he can’t build a robot or suit strong enough to resist the Man of Steel. But that’s okay, that’s not the point. The clues in the robot’s construction lead Clark Kent, ace reporter, to the WayneTech science labs. Just as Batman intended.
X-Ray vision lets Superman discover the Bat-Cave. He flies in - and every door and exit slams shut, with kryptonite-lined walls. Superman weakens, but isn’t down yet. He lunges for Batman, who grapples out of the way. Supes cuts the grappling rope with heat vision. Batman falls to the ground. The two men struggle, one weakening due to kryptonite, the other due to the fall and the injuries he’s taking from a still-superhuman opponent. It’s a race against time.
Finally, Superman realizes he’s out of time. If he doesn’t stop Batman, he’s going to die. And Batman realizes that Superman is going to make one final move.
He reaches for a pistol loaded with kryptonite bullets. And hesitates.
Superman warms up the heat vision. And hesitates.
As one, both men tell the other, “you win.”
And both of them now truly take the measure of the other.
There’s a long discussion in the cave, with the kryptonite shutters partially withdrawn. The two men finally leave peacefully. Not yet as friends, but no longer combatants.