My own notes and decks on what I've done so far and can contribute additional info towards:
Druid
The Final Frontier: I also tried Naga Sea Witch + Giants. Doesn't work. Seems to be hardcoded to Celestial Alignment, which is fucked up.
Buy One, Get One Free (of Taunt): I hated doing this one so much. My deck probably sucks but I was so angry at this nonsense I kinda refused to think about it any further. The big card you missed is Infested Goblin, that gives you 1-mana Taunt tokens to Broomstick. AAEBAZICBIUQ0eEDwuwD1qAEDcQG+waaB4EOoM0CntICv/ICoaEDnKQDlc0DmOoDrewDku4DAA==
Do it for the Vines: Please note that Solar Eclipse proc does not count as an additional cast per turn for this achievement! You need to actually play 5 Nature spells. AAEBAZICBOQI1hGMrgPR4QMN6QH+AcQGntICv/ICj/YC5boD7LoDm84D8NQDrewDtuwDtaAEAA==
Wear Your Sunday Best: If you run Invigorating Sermon as your only Holy spell, you can tutor it with Knight of Anointment. Also you can proc it twice with Archmage Vargoth, which reduces the amount of games needed. AAEBAZ8FBO0F/gf8/ALWmQMNnAL4B/sM97wC3sQC48sC2JgD+84DtuEDkuQDzOsD5+wDoaAEAA==
Spell Slingin' Savior: Try to proc it twice in one game to max out that efficiency. AAEBAZ8FAu0FtJsDDowB6AGcAs4D3QqMDtMWs8ECz4YD7IYD+ZMDlrYDysED9+MDAA==
Just between You and Me: The fifth secret can also be Autodefense Matrix.
Priest
Two Health Bars: Reno. Just play a Reno deck with some extra self heals thrown in against something like a Secret Mage.
Why Can't I Hold All These Cards?: Maybe my deck idea wasn't the best, but I just ran a bunch of token in hand generators to get to a full hand as quickly as possible and tried to stall with 10 cards in hand as long as possible. You can play cards that give you a card back in your hand without losing an Achievement proc next turn, and take careful note of which cards give you more than one card back in your hand so that you can play stuff and fill back up. Usually around 4-5 procs per match if the opponent wasn't aggro, in which case I would just concede immediately. AAEBAa0GBJIP2MIDtIoEtYoEDR7GzALo0ALF7ALJ7ALm7AKSgAPSiQO0kQOBsQPXzgP+0QPi3gMA
Rogue
Identity Theft is not a joke: To complete the achievement you need to get the basic Rogue hero power from Yoink!. This can only happen if your own hero power is already not Rogue's. You can either run two Yoink!s or if you only unpacked one copy like me you can use Sir Finley Mrrgglton. KEEP NOTES ON WHAT HERO POWERS YOU'VE GOTTEN ALREADY.
Just Don't Touch the Blade / Magnets, How Do They Work?: You can do both of these in the same deck, real easy. The trick is Cutting Class synergizing with your buffed poisoned weapon. Mix in Efficient Octo-bot procs and prepare a big Gadgetzan Auctioneer turn. Did it in one match. AAEBAaIHAq3rA67rAw7EAc0DpAfeB4YJ9bsCx84D99QDgeQDqesDq+sDrOsDkZ8Ekp8EAA==
Shaman
Extra Organic: Bru'kan isn't even that good. What you want is to play Beakered Lightning on a full board with a lot of Spell Damage thrown in. Rune Dagger makes things easier, Imprisoned Phoenix lets you set up in advance, Talented Arcanist gives you SD+2 same turn, Mad Summoner for when your opponent's side of the board is empty too. You can get 50 extra Nature damage per game, easy. AAEBAaoIAu0FkuQDDpwCvBTjuwKe/QKc/wLWnQPYqQOmywPNzgOH5APq5wOR6AOV6AOhoAQA
Warlock
Shadow of a Shadow: There are four 0-cost Shadow spells in the game already. Plus like you said, Thaurissan procs on 1-cost spells if you're lucky and your opponent is playing nice. AAEBAf0GAu0F1hEOowH7AZwCxAi2rALexALy0ALx9wKnmAPXzgPs0QPM0gOS5AON5wMA
What's Better than Two Imps?:Mad Summoner is your friend! Actually there are so many imp summoning cards, the way you're 'supposed' to get this achievement is SO much slower. Note the 0-cost spells thrown in this deck, they're actually to help you progress the other achievement while you're at this one. Probably should have thrown Ritual of Doom in there, but I forgot that card existed until later on oops AAEBAf0GApwC7QUOowHcBsQI3Q+2rALexALy0AKQ7gKrkQPWnQOdqQPXzgO84wOS5AMA
Warrior
Gym Buddies: You can also use Archmage Vargoth in lieu of drawing the second Bulk Up. Personally I ended up with a really fun deck revolving around spamming infinite Injured Tol'virs with Barista Lynchen. Almost burned my Bulk Up because I had so many Tol'virs in hand lol
Neutral
Everyone's in Here!:Overlord's Whip gives you one Gruntled Patron proc instantly without having to lose mana that turn. After that you just need two Frenzy procs from cards like Inner Rage, Whirlwind (not two though or you'll start killing Patrons), or Improve Morale. When you have one full health and three damaged Patrons on board it's time for the coup de grace: Sudden Genesis. ez game ez life AAEBAQcE1ATWEY/tA4egBA0WnAKiBP8Hv8MCo4sDhJ8D9sID9+MDkuQD1egDtJ8EoaAEAA==
Has Anyone Seen Mankrik's Wife?: I just stuck Mankrik in wild discard Warlock and waited to play it until my opponent was very low on health, making sure to trade disfavorably to make it seem like they had a chance. You only have to get lucky once, it took me three matches.
Top Secret Snoop:What if I told you there is a reliable setup for this achievement? This is my magnum opus. BEHOLD:
Constraint number 1: Opponent needs to have 5 cards or less in hand. Constraint number 2: They need to proc the secrets next turn. This is actually not that hard, because they WILL try to get rid of your minions, Cho especially, they can't even hit your face anyways. Constraint number 3: You need two Emperor Thaurissan procs, although this is not very hard because you run so many secrets that discounting two of them is trivial. To be totally honest, I did it without Millhouse since I just went for it because I was going to lose the next turn anyways, but if you give your opponent five free secrets they are almost certainly going to play them and free up some hand space.
I ran a bunch of different secrets to guarantee I would have five different ones to play, but PLEASE do not run Oh My Yogg! or Eye for an Eye, because they will either not proc or proc and fuck up the setup. Sacred Trial is also too inconsistent to get rid of on your side.
Here's the deck: AAEBAZ8FDIwByATXBu8I1hGLvQLA/QLY/gKOmgPb7gPQ9wPIoAQJnALPhgPshgP5kwP34wOS5AOY6gPP6wPu8QMA
Druid
The Final Frontier: I also tried Naga Sea Witch + Giants. Doesn't work. Seems to be hardcoded to Celestial Alignment, which is fucked up.
Buy One, Get One Free (of Taunt): I hated doing this one so much. My deck probably sucks but I was so angry at this nonsense I kinda refused to think about it any further. The big card you missed is Infested Goblin, that gives you 1-mana Taunt tokens to Broomstick. AAEBAZICBIUQ0eEDwuwD1qAEDcQG+waaB4EOoM0CntICv/ICoaEDnKQDlc0DmOoDrewDku4DAA==
Do it for the Vines: Please note that Solar Eclipse proc does not count as an additional cast per turn for this achievement! You need to actually play 5 Nature spells. AAEBAZICBOQI1hGMrgPR4QMN6QH+AcQGntICv/ICj/YC5boD7LoDm84D8NQDrewDtuwDtaAEAA==
Mage
Barrens Bubbler: AAECAf0EAA/CuAOBvwP30QOR4QOF5AOS5APQ7APR7APB8AP8ngT9ngTmnwTnnwTonwTpnwQA
Paladin
Wear Your Sunday Best: If you run Invigorating Sermon as your only Holy spell, you can tutor it with Knight of Anointment. Also you can proc it twice with Archmage Vargoth, which reduces the amount of games needed. AAEBAZ8FBO0F/gf8/ALWmQMNnAL4B/sM97wC3sQC48sC2JgD+84DtuEDkuQDzOsD5+wDoaAEAA==
Spell Slingin' Savior: Try to proc it twice in one game to max out that efficiency. AAEBAZ8FAu0FtJsDDowB6AGcAs4D3QqMDtMWs8ECz4YD7IYD+ZMDlrYDysED9+MDAA==
Just between You and Me: The fifth secret can also be Autodefense Matrix.
Priest
Two Health Bars: Reno. Just play a Reno deck with some extra self heals thrown in against something like a Secret Mage.
Why Can't I Hold All These Cards?: Maybe my deck idea wasn't the best, but I just ran a bunch of token in hand generators to get to a full hand as quickly as possible and tried to stall with 10 cards in hand as long as possible. You can play cards that give you a card back in your hand without losing an Achievement proc next turn, and take careful note of which cards give you more than one card back in your hand so that you can play stuff and fill back up. Usually around 4-5 procs per match if the opponent wasn't aggro, in which case I would just concede immediately. AAEBAa0GBJIP2MIDtIoEtYoEDR7GzALo0ALF7ALJ7ALm7AKSgAPSiQO0kQOBsQPXzgP+0QPi3gMA
Rogue
Identity Theft is not a joke: To complete the achievement you need to get the basic Rogue hero power from Yoink!. This can only happen if your own hero power is already not Rogue's. You can either run two Yoink!s or if you only unpacked one copy like me you can use Sir Finley Mrrgglton. KEEP NOTES ON WHAT HERO POWERS YOU'VE GOTTEN ALREADY.
Just Don't Touch the Blade / Magnets, How Do They Work?: You can do both of these in the same deck, real easy. The trick is Cutting Class synergizing with your buffed poisoned weapon. Mix in Efficient Octo-bot procs and prepare a big Gadgetzan Auctioneer turn. Did it in one match. AAEBAaIHAq3rA67rAw7EAc0DpAfeB4YJ9bsCx84D99QDgeQDqesDq+sDrOsDkZ8Ekp8EAA==
Shaman
Extra Organic: Bru'kan isn't even that good. What you want is to play Beakered Lightning on a full board with a lot of Spell Damage thrown in. Rune Dagger makes things easier, Imprisoned Phoenix lets you set up in advance, Talented Arcanist gives you SD+2 same turn, Mad Summoner for when your opponent's side of the board is empty too. You can get 50 extra Nature damage per game, easy. AAEBAaoIAu0FkuQDDpwCvBTjuwKe/QKc/wLWnQPYqQOmywPNzgOH5APq5wOR6AOV6AOhoAQA
Warlock
Shadow of a Shadow: There are four 0-cost Shadow spells in the game already. Plus like you said, Thaurissan procs on 1-cost spells if you're lucky and your opponent is playing nice. AAEBAf0GAu0F1hEOowH7AZwCxAi2rALexALy0ALx9wKnmAPXzgPs0QPM0gOS5AON5wMA
What's Better than Two Imps?: Mad Summoner is your friend! Actually there are so many imp summoning cards, the way you're 'supposed' to get this achievement is SO much slower. Note the 0-cost spells thrown in this deck, they're actually to help you progress the other achievement while you're at this one. Probably should have thrown Ritual of Doom in there, but I forgot that card existed until later on oops AAEBAf0GApwC7QUOowHcBsQI3Q+2rALexALy0AKQ7gKrkQPWnQOdqQPXzgO84wOS5AMA
Warrior
Gym Buddies: You can also use Archmage Vargoth in lieu of drawing the second Bulk Up. Personally I ended up with a really fun deck revolving around spamming infinite Injured Tol'virs with Barista Lynchen. Almost burned my Bulk Up because I had so many Tol'virs in hand lol
Neutral
Everyone's in Here!: Overlord's Whip gives you one Gruntled Patron proc instantly without having to lose mana that turn. After that you just need two Frenzy procs from cards like Inner Rage, Whirlwind (not two though or you'll start killing Patrons), or Improve Morale. When you have one full health and three damaged Patrons on board it's time for the coup de grace: Sudden Genesis. ez game ez life AAEBAQcE1ATWEY/tA4egBA0WnAKiBP8Hv8MCo4sDhJ8D9sID9+MDkuQD1egDtJ8EoaAEAA==
Has Anyone Seen Mankrik's Wife?: I just stuck Mankrik in wild discard Warlock and waited to play it until my opponent was very low on health, making sure to trade disfavorably to make it seem like they had a chance. You only have to get lucky once, it took me three matches.
Top Secret Snoop: What if I told you there is a reliable setup for this achievement? This is my magnum opus. BEHOLD:
Time Out! + Lorewalker Cho + play 5 different secrets + Millhouse Manastorm
Constraint number 1: Opponent needs to have 5 cards or less in hand. Constraint number 2: They need to proc the secrets next turn. This is actually not that hard, because they WILL try to get rid of your minions, Cho especially, they can't even hit your face anyways. Constraint number 3: You need two Emperor Thaurissan procs, although this is not very hard because you run so many secrets that discounting two of them is trivial. To be totally honest, I did it without Millhouse since I just went for it because I was going to lose the next turn anyways, but if you give your opponent five free secrets they are almost certainly going to play them and free up some hand space.