You don't need to win the tournaments to get the rare cards, by the way. You just need to get enough points to get a Platinum Pack. These packs have a chance to give you the rare tournament cards. It took me just over a year to get all of them, because RNG does not usually give you the rare cards.

You can get Platinum Packs from Open Tournaments, which happen every 2 hours. But it's extremely rare to get one from there. You will only see one drop after 50-100 wins. It's so rare that it's easier to just do the bi-weekly tournaments.