Well, that was fun. Who made that puzzle? Someone of this forum?
How I solved it:
The base cards were pretty obvious, especially as they were in order.
I: Trader was the next card, as it is the only trasher that can react to attacks.
Then I looked from turn to turn.
E: Moneylender was the next card as it has to be a card that gives $3 for trashing a copper in turn 4 of player 3.
G: In turn 6 of player 3, he bought a card with $6. As we see in turn 9: It's nonterminal.
So Grand Market came to my mind, and I looked and realized that it was bought with Copper in hand, but not in play. So, this was clear too.
A: This one made me curious. It seemed like a card which you let reveal always 4 cards of your deck and gives at least $4 as turn 15 of player 3 shows. I thought and thought and had to look in the card list. The only card that fit is Harvest.
C: was the best card in the puzzle. Of course it's nonterminal. In turn 19 of player 1 it gets drawn by the Grand Market and than itself draws two Silver. So I thought it has to be Laboratory. But then turn 17 of player 3 made me curious, as it gives $1 and a buy too. It took a while, but then I realized, it could be a level 3 City. I counted how many Cities where bought: all 10, so I was pretty sure now.
D: This one was hard too. It costs $2 as turn 1 of player 4 shows. It turn 12 of player 4 we see that it is non-terminal and draws a card (F wasn't in hand before).
And it has a option (with ^ and without). First I thought it is Native Village, but this didn't made any sense, especially in this turn, where he needed to put the cards from the mat in hand 2 times in a row. So this had to be Pearl Diver, which also took a while.
F: In turn 15 of player 4 we see that it gives a buy and at least $1. In turn 12 we see it's nonterminal and it gives at least 2 coins. Only Festival fits this criteria.
The attacks I try to solve at the end.
H: Turn 6 of player 2 showed a cursing attack that draws 3 cards. Only Torturer fits.
J: This had to be an attack which let everybody reveal a card and can also give junk to the opponents. Turn 5 of player 4 showed that it gives at least $2.
So it has to be Swindler or Jester. This was hard as the notation doesn't show which card the opponent got. But as player 4 had an 5/2 start I concluded this has to be Jester.
B: I know this is a cursing attack, which only got bought once for $5. In turn 13 of player 4 it draws at least 2 cards, so this is Witch.
BTW: At the time I was trying to solve the last card B, I found out that there is a solution link. That's kinda funny. So my walkthrough is somehow useless now. Nevermind. At least there is better solution for J.