I don't know about you, but there's a LOT to this event, and you will haveonly 839 days to get everything you want/need. Personally I want to get everything that the event has to offer, but I'll definitely prioritize that "Fang of the Fearless Cat" weapon for my Dark Knight.
Now, while we don't really know the rates of the medal drops, we can assume from the text for the normal medals that they will always drop on silver and gold, and I'm pretty sure we can assume that Gold will grant more than silver upon the completion of the Fate. I would guess you'd probably get 1 medal for silver and 3 for gold, which is normally par for the course for these events. When it comes to the number of medals for each YoKai though, I think that the event page has them staggered into a funnel. That's because they likely have tiers, meaning that while it may only take 10 medals to get the Jibanyan minion, it may take a 100 for the Manjimutt one.
Fortunately, I don't think that this is the case with Legendary Medals though since they are obviously NOT guaranteed to drop, and unlike the regular medals, I do believe they will only grant you 1 medal at a time regardless of whether you get gold or silver.If you take into account that there's only 8 days to the event that means there are only 199 hours of active in game time (barring any maintenance) that a player can work on the event. Even if they posed it as a challenge, I would bet that they wouldn't want players to spend more than 30 hours (unluckily mind you) grinding for these legendary medals. This leads me to assume that they either have a drop rate similar to the current state of the Atma grind (post patch) but require something akin to 13 medals per weapon, or they have it similar to the Luminous Crystal Grind but only require a single medal per weapon. Either way, it seems like RNG might be pushing people around quite a bit for this event unfortunately, but here's hoping that it only takes ~20 hours to get all the weapons.
EDIT: Completely misread the dates, 30 extra days practically guarantees that it will be on the level of the Luminous Crystal Grind and that it will take more than 1 medal for each weapon.