if you consider that half of people go out every round you can calculate (ok let's take tournament without qualification round, so with f.e. 64 or 128 players):

50% of player loose in 1st round - they have only 0 or 1 win for the quest.
25% of player loose in 2nd round - they have only 2 or 3 win for the quest.
12.5% of player loose in 3rd round - they have only 4 or in the best case 5 wins for the quest.

If to see to this calculation you see clear that 75% of people won't fullfill their quest with the first win and from next 12,5% of people it's depend if they loose 0:2 or 1:2 in the third round.

So I think, that more than 80% of player will not be able to fullfill quest in one tournament - they should wait for the next tournament.

How long they should wait ?

Ok let's take this moment we are now and look for the tournaments who are for regular cards (you cannot expect that somebody buy goldfoil-cards or alpha-cards only for solving the daily quest) and who are not Diamond Level (as this rule started in gold league and gold league player have to pay entrance fee for all Diamond Level tournaments I think such tournaments cannot count).

The last tournament (regular cards, maximum gold league) was 19 hours ago.
The next tournament (regular cards, maximum gold league) will start in 15 hours.

So their is a difference from 34 hours from one tournament to the next and with this you should fullfill your DAILY (!!!) quest ?