Alchemy is probably the most difficult set to fix, there's a relatively high percentage of duds (also due to the small set size), it's fairly impopular in general. Making it a full size expansion would be fun in my opinion, but it's probably not worth it considering the low popularity of the set.
Glossing over the individual cards, the ones that are obviously fine are Apprentice, Vineyard, Apothecary, University, Alchemist and Golem. The community seems to agree, none of those cards have more than 5 votes. The other ones are all debatable.
Herbalist is very narrow and it doesn't fit in the set all that well. The only card it combos with is Philosopher's Stone; in most cases you don't actually want to topdeck treasure, which is the main problem of the card. I mean, topdecking Potion is sometimes useful, but it requires a lot of luck and it's not worth it unless you have a lot of leftover terminal space. It could just be changed so that you can topdeck any card, like a terminal Scheme that doesn't draw, but gives +Buy and coin instead. Or it could become something else entirely.
Transmute is one of the worst duds in the game, about as bad as Scout and Adventurer, who also got the axe. Definitely needs to go.
Scrying Pool is difficult. It can lead to excruciatingly long turns, but the spying effect is interesting enough that I think it should stay on the card. It's also very strong, bordering on OP, but I think it's interesting enough for its strength.
I'd say Familiar could stay, it's certainly swingy but it's the only chance to ever have a cantrip curser. Any non-Potion cost would make it OP. And there are other swingy cards, such as KC and Treasure Map and Tournament. I mean, sometimes you need to have a bit of luck, and if you can't accept that you should probably stop playing Dominion and play chess instead. (No offense to anyone intended)
Philosopher's Stone is also a tricky case. It's weak, hardly ever useful, but the concept is just so interesting and unique. I think it would be a shame if it were to leave, even though I would certainly understand it.
Possession should just go. The concept of punishing a deck that's too good is interesting, but Possession just gives people headaches and it's no fun to play with, especially IRL.
So I voted Herbalist, Transmute and Possession.