Final Fight is a port of the arcade game of the same name. But unlike the arcade game, you can't just keep pumping quarters into it to brute-force your way through it, you have a finite amount of lives and continues to work with.
But you have a secret weapon.
At the title screen
Hold down the L button and press Start, and you get a hidden Option screen!
You get to adjust all kinds of things here: difficulty, extra lives, frequency of additional lives, there's a sound test to listen to, and you can even turn the 'Extra Joy' on or off.
I like to turn the 'Extra Joy' on.