Firstoff, we can make a long story short and say Bruce gets kryptonite and just uses it on him in BvS:DoJ, and thats his weakness.. so yeah. End of Story. That's not the point of this article.
Let's get into a realistic way of how Superman's powers work in the Man Of Steel DC Cinematic Universe.
Superman's powers must follow a set of rules for them to be realistic and for Bruce Wayne to be able to fight him, the rules must be definite and somewhere in the real realm of physics.
In Man of Steel, Jor-El explains to Kal-El that Earth's gravity is less than that of Krypton and the Yellow Sun powers him up. But there has to be more to it than that. So I present to you the following rules that apply to Superman in the Man of Steel and may apply in the DCCU to explain all his powers:
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Kryptonians possess seemingly Super Human Strength and Super Human Speed in areas with less gravitational force than Krypton
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Kryptonian Physiology is slighlty different than a normal Human, which allows their bodies to exert more physical force and endure forces acted upon it
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Kryptonian Biology is unique and allows for different radiations to be absorbed, manipulated, and repelled
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Kryptonians need extreme focus to manipulate their body and parts of their body to exert a force or change a force using the radiation energy that they have absorbed and channel it out
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Kryptonians under their natural Red Sun radiation seem powerless due to the absorption of that particular light spectra having a negating effect on their abilities to manipulate radiation
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Kryptonite radiation has a physical negative effect on Kryptonians by overloading their cellular absorption and causing a sort of very rapid radiation poisoning effect.
Stronger than a locomotive, faster than a speeding bullet, able to leap over tall buildings in a single bound..
Rule #1 partially accounts for his strength and speed, and rule #2 partially accounts for his physical endurance such as being bullet proof.
But I believe Superman's true power is #3, by absorbing Yellow Sun radiation he can channel that energy to create a thin force field around his body that can manipulate the surrounding radiation in the air around him. Having less gravity on Earth allows him to lift heavy objects and jump really high, but Superman manipulates the electro-magnetic spectrum to physically lift things and himself with anti-gravity force. This force also causes him to be more aerodynamic so he can fly around a lot faster and negate air drag.
You see this force before he flys in the sky as he kneels down, and stuff sort of floats in the air a bit, then a force is seen crushing the ground beneath him and pushes him up.
It's this same force that allows him to be bullet-proof and near invulnerable to physical harm, such as the burning fire in the oil rig, by creating that strong thin walled anti-gravity force.
It doesn't make sense for Superman only to be strong on Earth and being flight capable just because of less gravity. This would make it impossible for him to exhibit his powers in space, which he did in the movie. The thin anti-gravity force allowed him to survive in vacuum, to surive earth re-entry, and to propel around in space which of course has no gravity to begin with. Electromagnetic forces move in a straight line and the fastest in a vacuum. Superman needs a way to direct a force behind him, otherwise he would be floating slowly and randomly around in space trying to swim his way around.
X-ray vision, Heat vision, and why your Vision needs more Focus
Onto to rule #4, if you remember in the film, young Clark started to randomly exhibit X-ray vision. He wasn't able to control it as he had no focus and was scared. He didn't calm down until he heard his mom's voice and then it all stopped. It must take a "super" amount of focus to use his abillities and channel the absorbed radiation properly. You see him sort've calm down in the ocean as he's remembering his mom's speech, and then he suddenly blasts off in the water.
It's also important to note that Zod has a similar panic attack and gets an overload of Yellow sun for the first time, but increasingly got better with the use of his powers due to his military training.
The absorption of Solar radiation must be a passive thing and probably can't be controlled as well as other forms of radiation energy. Yellow Sun radiation must be that catalyst for the manipulation of other waves in the electromagnetic spectrum. And Red Sun radiation must be the inhibitor of that abiltity to manipulate it and channel in various other forms of the electromagnetic spectrum.
According to Wiki:
The electromagnetic spectrum, in order of increasing frequency and decreasing wavelength, can be divided, for practical engineering purposes, into radio waves, microwaves, infrared radiation,visible light, ultraviolet radiation, X-rays and gamma rays.
I bring this up because this explains his ability to manipulate and see in the other spectrums such as X-ray as it is a form of radiation in the larger electromagnetic spectrum. I also believe his Heat vision is actually a very very very very focused and concentrated form of microwaves manipulated by the physiology of his Kryptonian eyes turning Solar energy into heat energy. I believe so much force is concentrated in his pupils and exit so rapidly, that when it exits they appear to be "red" which is the first color of the visible light spectrum.
Super Hearing, Super Breath, and Super everything else
Super Hearing is all due to Kryptonian's natural ability and heightened senses. Sound is not an electromagnetic wave, so I don't think he manipulates sound. As for him floating in space ala Superman Returns and him listening to earth, that would be impossible due to sound needing to travel in a medium such as air. So more or less likely he is listening to Radio waves emitted from broadcast frequencies.
As for Super Breath, Superman must have a much larger lung capacity and stronger chest muscles to exert air rapidly out of his mouth to blow out fires and freeze things(and possibly super strong lips to funnel that air out properly.) He doesn't manipulate the temperature of the air, he just blows it out rapidly. You can try this yourself with a not so super breath. Put out your palm in front of your face and open your mouth a little wide, inhale deep, and blow a breath out as if you were trying to check the smell of your breath. Should feel warm right? Now blow as if you're blowing out a candle, and the air should feel cold. Now move your hand closer to your face as your blowing out wind, it should start to feel warmer the closer you get to your face.
Every other ability that doesn't account for radiation manipulation and anti-gravity forces is just natural Kryptonian ability of being really good at mundane things like hearing, blowing-air, or styling his hair really good.
" I want you to remember Clark, In all the years to come, in your most private moments, I want you to remember my hand at your throat, I want you to remember the one man who beat you."
Bruce is proably going to use all of this knowledge to his advantage and probably use a simulated Red Sun radiation to neutralize Superman. He could possibly also use the material from Zod's ships which could carry materials or elements from Krypton that carry the proper radiation to poison Superman with.
So Batman has three options to handle Clark and his extraterrestrial abilities.
By using Red Solar Radiation he will inhibit Clark's ability to manipulate the other spectra and cause him to be vulnerable and seemingly powerless. Not sure how much this will affect Clark's normal strength and speed on Earth due to less gravity than Krypton. He could still have the agility and still be able to pack a punch, but without the invisible force shielding him from harm, I don't think he'll be able to withstand a couple of well placed punches from Batman.
On the otherhand, with Kryptonian radiation and its radiation poisoning effects weakening Superman, he would have Clark on his knees slowly dying. This seems more like a last resort type of thing as for it to be a real battle, Clark has to be able to fight back at least a little bit.
The third and final option I think I could see play out, is using Batman's own intimidation. It's Batman's greatest power besides his genius, his raw presence is meant to strike fear into his enemies. Just as Rule #3 with Clark's ability to absorb as his greatest power, Rule #4 might be his downfall if Clark has to really focus to use his powers properly. Imagine, Batman using his mind, his cunning, his gadgets and his element of surprise and instill fear to make Clark cower like a small child in a cape playing hero.