Does anyone know about the nature of these missions? Are they too hard? What do they involve?

You have to beat your opponent with 1 character only (the champion) and at least 15 cards.
The opposing characters are comparable to the standard other bosses, customized for the champions of course.
Don't expect easy win...

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Collectionneur de cartes

is it true that you need to have 1300 wins with the respective champ's guild?
like 1300 wins for a kotoba deck for daijin, etc...

no