No Black Market - so no Potion, since we can't have Potion-cost cards in the Kingdom, no Events, and no gains other than as a result of buying a single card:
Kingdom:
Charm, Haggler, Catacombs, Cache, Cultist, Bazaar, Trader, Young Witch, Skulk, Watchtower (Bane), Smugglers; Shelters
Deck: 8 Cultists, 8 Bazaars, 7 Hagglers, 6 Charms, 1 Necropolis, 2 Catacombs, 1 Trader, 1 Watchtower
(Trader can trash Coppers, and with a Watchtower in hand can trash Shelters).
The trash contains your 9 starting cards, plus two Silvers from trashing the Shelters.
Your opponent's deck consists of their starting cards and a single Smugglers.
The bottom two Ruins are the same.
Play 8 Bazaars and a Necropolis, leaving 10 actions, leaving a hand of 4 Cultists.
Play 8 Cultists (chained) and 2 Catacombs, leaving 7 actions and drawing 22 cards. You need to draw 4 Cultists, 2 Catacombs, 7 Hagglers, 6 Charms, 1 Trader, and 1 Watchtower = 21 cards, so this works.
Play 7 Hagglers, so you now have no actions.
Play 6 Charms, always taking the gaining option.
Buy Duchy
Gain from Charm: Charm, Haggler, Catacombs (reveal Watchtower to trash, gaining Estate), Cache (reveal Trader to gain Silver instead of one Copper), Cultist, Bazaar
Gain from Haggler: Watchtower, Trader, Curse, Young Witch, Skulk (gaining Gold), Smugglers, the penultimate Ruins.
There are 19 Supply piles, of which only Province does not cost $6 or less, and your opponent can Smuggle from any of the 18 other Supply piles.