reference, reference, reference. Put together a solid reference video of what you want your fight to look like. put together several videos, cutting up the punches and kicks you want. Even the most exaggerating parts of a fight can still have real life reference. Just gotta find it!
If you're going into some over the top or superhero-ish fight animations and are looking at live action movie references, be aware of cables used to pull actors back after being power punched in the face. When animating always make sure to know where the force is coming from so you can work with a reference like that without accidentally copying the fake throw haha.
Otherwise, @slipsius ' advice is spot on. A nice trick is to take your combined references into one video, put it in Maya (or whatever software) on an image plane, set a key for the image plane on your timeline that fits your key and other important poses, go to your graph editor and set the keys to Step mode. This way you keep only the important parts of the ref and you can easily retime it by moving the image plane's keys around.
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Watch kung fu movies, choreography plays a big part in making a fight scene seem more dynamic.
Otherwise, @slipsius ' advice is spot on. A nice trick is to take your combined references into one video, put it in Maya (or whatever software) on an image plane, set a key for the image plane on your timeline that fits your key and other important poses, go to your graph editor and set the keys to Step mode. This way you keep only the important parts of the ref and you can easily retime it by moving the image plane's keys around.