Crusader Kings III

1) Easiest solution: Maxing the hastiluder wit track

The easiest track of the Hastiluder trait to max out is the "wit" track, because once you have gained the hastiluder trait by participating in at least one competition in any tournament, you can earn experience for the wit track outside tournaments by challenging other characters to board games, which you can do once a year provided you select a different opponent each time. You still need to unlock the "challenge to boardgame" interaction the usual way first, i.e. by either picking the "befriend" perk from the diplomacy skill tree or by having the tabletop warriors cultural tradition.

You'll earn experience no matter whether you win or lose, so your character doesn't even have to be good at the boardgame minigame to max out the wit track.

The one tournament you need to visit to gain the hastiluder trait in the first place doesn't need to have a wit based contest (the recital and the board game contest), but it is much less tedious (and feels much more earned) to participate in one or both of those wit-based contests and win or at least make it to the finals, which will give you a huge chunk of experience in the wit track. The recital contest mostly uses learning and diplomacy checks, so you should have very high scores in those abilities if you want to win a contest. Board game contest uses learning, but also makes use of pretty much all stats except prowess, often given you an alternative which stat to rely on, so a genius character with overall good stats will do best. You can be either gender for those contests.

2) Alternative: Maxing the hastiluder foot track

This is much more difficult and risky than maxing the wit track, so I wouldn't recommend it unless you want to go for the achievement to max all tracks with the same character or you absolutely want to do it with a fighting discipline for roleplay reasons. This track can also be maxed out by participating in only one tournament and then earning more XP by fighting personal duels (only duels that trigger the duel minigame will give you experience, not random events that narratively suggest that you fight a duel, but are only resolved with a single prowess check instead of the duel minigame). Fighting opponents that are on your skill level or above gives you more XP than fighting pushovers, but of course also comes with a greater risk of injury or death.

Your character for this needs to be of the martial gender (which is male only for most cultures), he should of course have a very high prowess value (If your character's prowess is only mediocre, good sword and armor artefacts can help a lot), he should be very healthy (so he has better chances to survive and recover from injuries) and he should have either personality traits or cultural traditions that unlock duel interactions, such as:
- the chivalry tradition (unlocks friendly sparring with knights)
- the martial admiration tradition (unlocks duell challenges)
- the wrathful trait (unlocks the "punish criminal" interaction against criminals, leading to a duel to the death with a criminal - you don't necessarily die if you lose, most of the time you just get wounded and lose your punishment reasons against the winner, but you can be killed in this)
- the irritable trait (unlocks the unleash your anger duel interaction to beat up any character you don't like at the cost of some tyranny points)
- the trial by combat or performative honor tradition (requires Northern Lords DLC and North Germanic culture, unlocks challenging criminals whom you couldn't decide to imprison (due to them not being your subjects or you lacking the necessary level of crown authority) to judicial duels, either for death, gold or humiliation (inflicting stress). I strongly recommend the gold option unless you really urgently want the other character dead, because if you chose a duel to the death, your opponent will 100% kill you if you lose)
- the stalwart leader perk from the gallant skill tree (unlocks challenging rivals to a duell, inflicting stress)

Aside from those character traits, all characters of the martial gender who have artefact claims can challenge the owner of the artefact to a duel for it (Owner might refuse if their prowess is too low or they are a cautious/cowardly person).

3) Alternative: Maxing the hastiluder horse track

This is more difficult than the two prior ways and will likely require you to participate in multiple tournaments. Don't aim for this track unless you also aim for the Sir Lance-a-Lot achievement or the achievement that requires you to max all tracks.

You gain experience for this by participating in the horse race and joust contests during tournaments (the latter requires you to be of the martial gender). You gain a little bit of experience outside of tournaments (after you have participated in at least one tournament to unlock the hastiluder trait) each time you complete a journey (any travelling, but only once per travel) and each time you personally command a non-trivial battle. Participating in a hunt that involves chasing after the game on horseback also gives some hastiluder horse XP). The XP gain for those actions is so small though that you will likely not be able to complete the track by those actions alone, you will have to do multiple tournaments.

EDIT: I'm not sure about the "command non-trivial battle" part. I'm 99% sure that I did receive horse XP for commanding a battle, but it isn't reproducable, the battle being non-trivial might not have been what triggered it. Maybe you need to own a personally trained warhorse (you can get one by a random ruler event from the martial event line) or maybe you need to lose the battle and flee ("A horse! My kingdom for a horse!" ;-) or maybe it is tied to having certain cultural traditions that are linked to cavallery warfare.

I recommend to avoid jousting and prefer horse races until the track is full and you do that one joust that is required for the Sir Lance-a-lot achievement, because jousts have a high risk of fatal accidents even for characters with very high prowess.

4) And what about archery?

This one is the most difficult to max out, so don't bother unless you go for all of them. Outside of doing archery contests in tournaments, AFAIK only scoring succesful kills with the bow during hunt events will gain you experience for this (which is very unlikely unless you host the hunt yourself). Since tournaments are very expensive, NPCs don't host them very often and when they do, they have a tendency to give annoyingly short notice (so you often can't even reach foreign tournaments in time unless they are really close by) and they won't always include an archery contest, so the only way to max out this trait is to host multiple expensive events yourself.