One great 'Batman and Bane Fanfiction' is 'The Redemption of Bane'. It shows a different side of Bane, exploring his possible path towards redemption. The author does a great job of delving into the complex relationship between Batman and Bane.
In the comics, Batman doesn't die at the hands of Bane. Bane is a powerful adversary, but Batman finds a way to overcome his challenges and live on to fight another day. Their confrontations are epic, but Batman's resilience prevails.
Well, Bane achieves this by outsmarting and overpowering Batman. He uses his raw strength and strategic planning to inflict a severe injury that incapacitates the Dark Knight.
Batman defeats Bane through a combination of physical combat and mental tactics. He trains hard to improve his strength and endurance and then uses his knowledge of Bane's fighting style to gain the upper hand. Also, he sometimes gets help from his allies.