I'm going to post ideas for how the Spirit battles could work.
Irene Lew:

on Wrecking Crew
Jo Hayabusa:


on Frigate Orpheon (referencing the boss fight in the NES Ninja Gaiden game)
Jaquio:

(will suddenly have a Final Smash) on Dracula's Castle
Robert T. Stergeon:

on Luigi's Mansion
Rachel:

(Golden Hammer equipped)
Muramasa:

Hayabusa (will heal after taking a lot of damage) on Smashville
Murai:

(x4) (will have a Final Smash after taking a lot of damage) on Find Mii
Doku:


(x2) on Castle Siege
Genshin:


(representing Elizebet) on Sky City Tokyo
Momiji:

(with enhanced speed) on Guar Plain
Kasumi:

on Sky City Tokyo (stamina match)
Ayane:

on Sky City Tokyo (stamina match)
Mizuki:


(representing Canna) on Fourside
Epigonos: Hayabusa x2 (both equipped with Death's Scythes) on Arena Ferox
Ken Ishigami:

on Shadow Moses Island
Regent of the Mask:

on Fourside (stamina match)
Yaiba Kamikazi: Hayabusa (metal) on Sky City Tokyo. (stamina match)
This is all I can think of for now. I'm sure there are better ideas but I at least want to get these out.