A fight animation is an action-packed short animation pitting two groups or factions, usually of the Five Nights At Freddy's variety, against eachother in physical combat.
Usually I'm given a white card, only confined to what factions fight it out and what location. In my process, I incorporate certain personality traits in the way characters go; one might be more reckless while others more reserved. Along with that, I also consider the 'power level' of characters, wherein the more archaic and esoteric characters of the series are usually more powerful. Or possess magic/telekenises or something like that.
Generally this type of content is 'mindless', as no specific story is present. Despite that, I attempt to vaguely justify the situation and reasons for combat yet this no specific necessity.
Fight animations are notoriously tricky to manage due to the labor of animation-work required for little actual runtime, which makes it less profitable logistically. For that, I usually try to incorporate a story or trickery nonetheless; to pad runtime and add more substance.
SFM
After Effects
Photoshop