How can I mulligan to a single card and still win?
Solution 1:
The easiest, yet by far most cheap and tedious, way to unlock this is to go to the Weather the Storm encounter in Shandalar. Mulligan down to one and then simply don't play anything, not even land. The encounter has no creatures, and can only damage you through the cards you play. As a result, it will simply play a second Aether Storm as soon as it can afford to, and then mill itself down to 0 playing land for the rest of the game.
Solution 2:
The nature of this challenge is to both amplify the importance of lucky draws and significantly slow your development: the one-mana creatures of e.g. Avacyn's Glory can be played on turn 2 at the earliest, two-mana creatures on turn 3 at the earliest, and three-mana creatures on turn 4 at the earliest—but these three scenarios are mutually exclusive! Each creature you cast deprives you of the opportunity to draw a land, and each land you play deprives you of the opportunity to draw a creature.
Because of these limitations, the player will have the greatest luck with a fast deck like the aforementioned Avacyn's Glory while playing against an opponent or encounter that's slower, such as the Cultist encounter or the Mul Daya deck.
Special consideration should be given to the final encounter in Kaldheim, because
your teammate Chandra will help stall the enemy offensive while you draw and play your initial lands.
By playing Avacyn's Glory in that encounter, I was able to successfully unlock this title after several attempts.
Solution 3:
The easiest way is run the mono blue deck as a hyper-aggro illusion deck. Get rid of all cards that cost more than 4, and load up on as many 1 and 2 drop creatures... Don't run any counterspells/enchantments, or cards that require certain conditions, but ovinize, unsummon, and frost breath are all fine, but everything else should be creatures.
Then play the Rumble in the Jungle encounter on Alara... I won it on my first attempt, but a useful strategy is to mulligan down to 1, and if it's not a land, or you don't get a land on your first draw, then go ahead and restart the duel.
I have tried to unlock this persona using multiple decks and playing against numerous opponents/encounters, but I got it on the very first try playing Rumble in the Jungle on a mulligan to 1.