Trade only? : yes, you go first
my personal ranking would be (excluding togwaggle since I've had the luck to not have faced him):
1 - The darkness - even with the free board clears, unless you have recovery, taunts, or just a very strong board, this is very difficult. Since these bosses have very high health, aggroing them down is ineffective, and the darkness's constant stream of 5/5s capitalizes on this fully. Unless your deck is capable of churning out a lot of board presence every turn, you're just going to die.
2 - Xol - not that hard but you have to be extremely careful when she has beam of confusion in hand - I once lost a game to her when she stole my wax rager and proceeded to tear me to shreds. Other than that worry she's not enormously threatening. once she gets the quest she has a constant board but it's not really that big. It's safe to say that if she didn't announce her beams as she got them, she would be much more difficult. As is, not so much.
3 - Azari - Seemed extremely threatening at first, but since he does so much damage to himself, aggroing him down isn't too hard. High value in your deck is important for this one, but either way with enough brute force he'll kinda just die
4 - vustrasz - absolutely trivial, I have never lost to vustrasz. His board space is severely limited by the master chests, so you can rapidly take a huge board advantage, and there's very little he can do to you. Board clears are bad, big minions are good. Even if he buffs the chests, just ignore them - even with the buffs he can't beat your board advantage, just keep hitting him until he dies.
I considered northshire cleric, but it turns out 2 mana draw a card is terrible compared to 0 mana draw a card, and I essentially never used it. That said, I agree getting rid of roc is good. I ended up replacing it with arcane giant, which worked really well, but I wanted to keep the decklist on here super cheap.
as for losing stoneshaper, I disagree. The whole point is to create a strong wall to keep your elementals alive till you play the auctioneer. Also it synergises if you end up playing a radiant elemental turn 3. I don't think it's crucial like tar creeper, but it's definitely useful. Also, spell damage, as it turns out, just isn't that useful. I ran thalnos at one point and he ended up being a dead card. Since you go infinite anyways, there's not much difference between 5 mindblasts and 6.
I've been having a ton of fun (and success) with this decklist I came up with. Unlike most of the decks I've seen for the brawl thus far, it's super cheap (360 dust in total, no epics or legends) and is highly effective, often achieving victory on turn 5 or 6. If you want to get a good deck to grind gold on tavern brawl for cheap, I highly recommend it.
for each prep pod, there's a shadowstep pod making it worthwhile. It's a little inconsistent, but it's consistent enough, and sometimes it's just amazing.
which is why Flame Elemental, and the cards that create them, are so brilliant. What do I care if you pull out and kill my Fire Fly? It's the Flame Elementals that matter, and by that point I'll have like 3 in hand.
I agree with basically everything you say here, except about edwin.
You claim that edwin is antisynergistic, but clearly, you've never played him. Crystal core only ever makes edwin a 5/5 if he is in play when crystal core is used. If you play him after crystal core, his boosts are applied after crystal core takes effect. Basically, what you've got is normal edwin, with an additional +3/+3 boost. 9/9 edwin is really easy, for example.
What this means is that edwin is perfect as backup. Deck doesn't turn out, don't get crystal core? edwin can still drag your bleeding carcass to victory. Board cleared after crystal core, running out of puff? edwin has your back.
And yes, that does mean that very occasionally, I draw him and it costs me the game, but the number of games that he has cost me is nothing compared to the number he has dragged out of the ditch.
Edwin, and edwin alone, is worth having of those cards, for this reason.