Drop out of World of Light every 3-4 fights to get a new character challenge, they don’t “stack” so be sure to back out of WoL frequently to not miss them. IIRC every time you lose to them, they get knocked down a little in difficulty.
Another slightly confusing system: spirit fighting style training. There’s about 10 trainers in all, three of which don’t show up until waaaay later in the WoL campaign. A single spirit can learn all styles, but only have one active. After learning a style, if you take it back to the gym, it’ll toggle that style back on.
Using the “Forget” gym will just toggle off any active styles, it doesn’t wipe that spirit’s learned styles or anything. If you fuse a spirit though, the resulting fusion will not inherit any of the learned styles (to my knowledge).
After you send a spirit to the leveling gym, style gyms, or on treasure hunts, there’s a cooldown period of about 10 minutes where immediately sending out that spirit will have slower results. From what I can tell, there’s no reason to have a spirit trained in all styles, but I’m doing it anyway since it’s a fun distraction.