So, base set act 3 game 18 is pretty ludicrous, in a bad way. You're up against someone who starts with a Province, Duchy, Estate, Silver, 3 Coppers and 3 Witches. You have a standard starting deck but you get a free phantom Throne Room play at the start of each turn.
The kingdom is: Chancellor, Village, Workshop, Feast, Moneylender, Remodel, Throne Room, Festival, Laboratory, Witch
Basically, everything there just works to dick you over as much as possible. He's going to open Village or Festival, and usually play a Witch on turn 1 and 2 Witches on turn 2, and will also grab Throne Rooms to let him probably put all 10 curses into your deck by about turn 6 or 7. The only trashing is Remodel and Moneylender, and there's no defence against the Witch otherwise. After he's cursed you to death, he'll sometimes remodel the Witches, usually buys gold, and starts slamming down on the Provinces from about turn 9 or 10, during which time you're dealing with having 20 junk cards and probably only a handful of decent cards to deal with it.
So far the only even vaguely reasonable strategy I've found is to resign turn 1 until you get a 5/2 start, preferably going first (yes, that's random as well, for some inexplicable reason), and then open Witch/nothing (yeah there's nothing at $2 to help in this case either, any of the base game $2s would have been really helpful here), and hope that you can play your Witch twice before the curses run out in order to go 4/6 on the curses. If you manage that, and follow up with good play (Moneylender is great, Remodeling curses is surprisingly helpful, Thrones, Labs etc.) you have a decent chance of losing by less, and a small chance of actually winning. It took me quite a few tries to actually get through.
Edit: Thanks to the advice of PST and DXV, I've posted a strategy that wins maybe 1/4 to 1/3rd of the time, which is still frustratingly low but good enough to get through.