There's always a simpler way, but it takes a lot of experience to do this stuff.
There are programs that allow bone based animation in 2D, using body parts and animating things smoothly. It might be the best option for a 2D fighting game these days.
It would be possible to get a 3D model of a fighter and animate it, then render the animation onto a spritesheet. Drawing a sprite is fairly easy, drawing 200 frames of animated sprite is really difficult. It is easier to animate in 3D then render, than to just draw everything.
For StreetFighter2, they used traditional flip page drawings, every frame of animation was drawn first, then scanned and made into a monochrome pixel drawing, and coloured after that. That's a really old school method that probably took hundreds of man hours - but it allows a lot more fluidity than new techniques allow, hair flopping about, clothes moving convincingly etc.
The bottom line is that you or someone has to be able to animate, not just draw but be able to make convincing movements. It has to be planned, you have to sketch out each animation, and be prepared to spend a lot of hours on it. The only people who make truly great 2D sprite animations, are those with a passion for it - if you don't find it fascinating, then you just won't get it done.
The final solution, well go retro!
Use 32x32 or 64x64 pixel sprites for the fighters, with a small resolution like that it takes far less time to draw and animate sprites, and by it's nature, it's ok if movements are a little mechanical, it's kinda expected. People who like beat-em-ups probably played and enjoyed the old school fighting games, like IK+, Fist, Last Ninja, Yi-Ar Kung-Fu, Double Dragon. I tend to prefer these to the new SF and MK games, before fighting games turned into a memory test of button combos.
I am the one who knocks...