DISCLAIMER: I don't own the Avengers or the Justice League.
Batman watched from the rooftops as a woman with red hair, wearing black leather, beat a gang of thugs to a pulp. She then went through the pockets of the boss, taking some kind of documents from him.
Batman dropped down, using his huge cape as a parachute, landing silently a few paces behind the woman. The woman turned to face him, looking bored. "A good entrance, bat boy, but I knew you were there from the start."
Batman moved closer, trying not to look particularly threatening. "Who are you?"
The woman also moved closer, and her movements slightly reminded him of Cat Woman. "I don't think that's any of your business, Batty."
Batman folded his arms, hoping to negotiate. "I was looking for something those criminals had. Not those documents. Something else."
The woman smirked. "A green crystal? Widely known as Kryptonite?"
Batman started, surprised by the woman's knowledge. "Kryptonite is very dangerous."
"We know exactly what it does. We also know some good uses for it."
Batman acted as if he was about to say something, but instead slid across the ground at the woman, attempting to kick her feet from under her. The woman jumped into the air, jumping onto Batman and wrapping her feet around his head, attempting to break his neck. Batman Tasered the woman's leg, before kicking her off himself. Batman faced her, and she had already recovered from the Taser. She jumped at him, swinging her foot into his head. He punched her back, and jumped into the air and kicked her head downwards. She slid along the ground and attempted to kick him again, but he jumped over her, and she jumped up from the ground, kicking him a few times in mid-air. Batman grabbed the woman by the leg and threw her face first to the ground.
She recovered quickly and charged just as he landed, but he kicked her back to the ground, before firing his grapple at her. She dodged the grapple, pulling a knife and attacking. Batman charged also, throwing batarangs as he moved. She dodged the batarangs, dodging three before the two fighters crashed into each other, and Batman tackled the woman to the ground. He tossed a flash bang grenade into her face, blinding her, closing and covering his eyes to avoid being blinded also, before releasing her and Tasering her again. She struggled, but Batman kept hitting her with the Taser, before finally kicking her in the face, stunning her. Batman placed a set of cuffs on the woman's wrists, and another on her ankles. He then searched her for identification and more weapons, finding a knife, and a card. Her name was Natalia Romanov, alias, Black Widow, and she worked for an agency called SHIELD.
Batman stood in the room with the handcuffed Black Widow. "What do SHIELD want with that Kryptonite?"
Black Widow stayed silent, and Batman slammed his fist on the table, but she still was completely unshaken. "If SHIELD take the Kryptonite, they'll be making an enemy of the Justice League. Not a good idea, I'm telling you."
Batman picked Black Widow up, glaring at her. "This is serious. Kryptonite is not something we're gonna let you take. Your people are not getting it."
Reasons for this outcome: 1. While Black Widow is easily one of the best non superhuman fighters in the world, Batman has trained himself to the utmost height of human possibility, so much as to be essentially a superhuman himself. 2. Batman's armour has been shown to protect him from bullets, while Black Widow only wears leather. 3. Black Widow has been shown using weapons in battle, but Batman's weapons are numerous and very effective. His wide ranged arsenal would give him a massive advantage against Black Widow.