don't even need to read ahead nor is it spoiler, because this was already explained in full in past chapters LolAfter reading ahead and knowing a very similar skill/level system from an mmorpg i used to play (like seriously everything felt practically one to one) I think I can explain. Technically spoilers, but in the sense that I'm spoiler-ing the rules and not plot stuff.
Anyways, the skill trees for martial arts skills basically go [Main attack style (archery, martial arts, swordsmanship, etc)] as the main umbrella so to speak => [9 different types of attacks/skills named after shogi pieces unlocked by doing certain actions involving the attack type] Said attacks/skills under the Archery umbrella are things like "strong single hit" and "rapid fire" and so on.
For each of those 9 types, there are levels you can upgrade them to using experience/points gained by leveling. If I recall there are 25 levels per skill, going from 16th Class to first Class, then 1st Dan/Grade to 9th Dan/Grade. In order to compete in the title match of your preferred style (Archery, Swordsmanship, Shield arts, etc) you would need to have the max level for each skill. So if you wanted the Archery competition, you would need 9th Dan in all the shogi piece named skills for archery.
Relatedly, in magic, things are similar in that there is an "umbrella" of skills for each element (fire, water, wind, earth, lightning) but instead of shogi terms they use... well im not sure exactly but I think it's martial arts. I sorta just know they're 5 of them per element and go something like "4th form" and "5th form" (forms 1-3 have a real name attached to it but I can never remember off the top of my head). Interesting to note, there isnt a title match exclusively for fire magic or anything, just magic in general, so the requirements here are to have one magic element with all their skills at max 9th Dan.
And that's about it, feel free to ask clarifying questions
and multiple chapters' comments after have people explaining it again, too