I just looked at the top, and one answer is 'tunnels'. I've actually done the sims before because I've played pure minion against minion-tunnel before, and wanted to know which is actually better. Minion-tunnel wins in the sim against pure minion, by like 55-45.
Remember, all 8 tunnels give him 16 points - same as 2 provinces. And they also give him gold when you play your minions.
So if you go basically pure minion against minion-tunnel, you have to play pretty crisply - it'll come down to a few buys here and there, and you're actually starting out at a strategy disadvantage. Still winnable, of course, but it doesn't take much bad luck or misplaying for it to go the other way. You need to keep hitting $5 exactly, whereas he's okay with drawing 3 (for tunnel), 5 for minion, or 6 for gold, and he can make much better use of the terminals around.
Having good terminals around (wharf!) also favors Minion-tunnel, because it's easier to stick terminals in a deck that's fat with gold and avoid collisions.
The Festivals definitely helped you, they were like 2 more minions. So that's good. Festivals are good for Minion.
I think the Secret Chamber buy was a mistake. Against Minions, it's pretty hard to use the SC right, because you don't know whether you'll have to discard your hand or not... Did it end up helping you the times you used it as a reaction? It definitely tricked you into getting a turn-11 silver, that wasn't good.
On the other hand, you again didn't get any Havens. I think I remember making a comment about Havens in one of your previous games, too. Havens are pretty good, man! They're cantrips, so they help you find your Minions better, they don't get in the way, and they can smooth out draws. There were even a few times when you didn't buy havens on turns when you played 3 coppers and bought nothing! You seem to have something against Havens. Get havens.
So, to summarize:
1) Minion/Tunnel is good, so don't think you had the tactical advantage because you got 6 minions. You were at a disadvantage because he got 8 tunnels. But even once you've picked your strategy, since you're going for pure minion, you did some things wrong...
2) Big mistake, IMO: you didn't get any havens.
3) Your black market was basically a silver that took an action. You never once used its ability. What were you looking for in the Black Market deck? Was there like a mountebank in there or something?
4) In addition to starting cards you had 5 non-cantrips that you got on the way to Minion - 1 secret chamber, 1 black market, 3 silvers. That's too many. On turn 3, you could have gotten a Feast instead of a Silver, from your Black Market - feast is good! It turns into a minion and then goes away! Some of those, perhaps 2, could have been Havens instead. Would make for a more resilient deck.
Oh, and one strategy option you guys both missed - Fairgrounds. With Black Market around! Again, favors Minion-tunnel, because if he noticed, his gold-filled deck would be much better suited to a long fairgrounds game than yours.