I'm not sure about Jade Idol for the 30 health challenge, primarily because that requires you to get to 30/30 Jades, which most players will concede well before that happens. My best guess is to double the stats on Walking Mountain with Therazane then do Conductivity --> Criminal Lineup to fill your board with 8/32 Walking Mountains, but that is absurdly expensive (19 mana in Shaman) and I feel like there's got to be a better way.
I'll add the Clefthoof one though. You can do it with Baleful Banker with Amplifier and a single Thaurissan discount.
They added a bunch of new Achievements themed around the older expansions with the most recent update. And they're some pretty neat little puzzles to solve them instead of the regular "Play 1,000 Dead Seagulls" so many of the newer achievements become. So I'll list them all here, as well as some solutions to achieve them. If you have other potential solutions, as well as solutions for any I didn't find one for, feel free to comment below.
Note: Many of these combos require more than 10 mana. However, these are all Wild-exclusive achievements, and as such, there's a lot of Wild exclusive mana cheat/ramp effects we can use to make them easier. Even if they don't need it per se, cards like Emperor Thaurissan or Wildheart Guff will make this process much easier.
Rise of Shadows:
Cast Plot Twist and end up with twice as many cards as you started with.
Chromaggus into Plot Twist when your hand has 5 or fewer cards.
Have a friendly 0-Cost minion in a Duel! and survive.
Two solutions: Either cast Duel! when your opponent has a full board, or while you have a Footman as your rightmost minion. Either way, your deck needs only 0-cost minions at the time of casting Duel! for this to count.
Hold onto it for a long time then play it into a wide board. Mad Summoner can be used to help. You can use Mo'arg Artificer to double the damage dealt.
They can't attack if they weren't summoned. This can be easily done with Li'Na, Shop Manager, but you can do something similar with Violet Teacher provided you're at 6/7 board slots.
Summon 7 of the same Murloc with a single Tip the Scales.
As a reminder, Ra is summoned by Mogu Cultist and controlling 7 of them when the Battlecry triggers. Charge is a worthy consideration because many players will either kill your Ra, or immediately Concede if they can't.
End your turn with 7 minions that each have 30-Health or more.
Destroy exactly 5, then exactly 2 minions with a single Earthquake.
Surprisingly there's currently no way to discount Combo cards. Record Scratcher can be used to refresh lots of mana, making it easier to play all the Combo cards.
Descent of Dragons
End your turn with 6 of Chenvaala's Snow Elementals in play.
Draw a Dragon while not holding one with Breath of Dreams 2 times in one game.
Cards with Dredge can make this more reliable.
Guess correctly with Envoy of Lazul 3 times in one game.
There's some luck and skill here. Either be good at hand reading and figure out what exactly your opponent would be holding onto, or just get lucky. If your opponent has one card in their hand though, that's your cue to spam Envoy as much as you can because you know what the card will be after the first one. Some amount of minion duplication/bouncing is required.
Destroy the enemy hero with one of Nithogg's Storm Eggs.
End 4 consecutive turns with MORE than 10 cards in hand as a Warlock.
Complete Clear the Way with the 4/4 Gryphon summoned by it.
Complete the first Clear the Way, then Youthful Brewmaster the first Gryphon. Play the second Clear the Way and 2 other Rush minions, completing it with the Gryphon.
Ashes of Outland
Draw (but don't discard) 3 cards that aren't spells with a single Fungal Fortunes.
Locations, Weapons, Heroes. Druid can (at the time of writing) put 9 copies of locations, 4 copies of Weapons, and 3 Heroes into their deck.
Play a "Deal 8 damage" spell on an Artificer when there are 7 Artificers on board. A potential combo is to Artificer --> Conductivity --> Criminal Lineup --> Torrent
Spend 8 Mana in a single turn before your 5th turn as a Warlock.
Darkglare Warlock is basically designed to do exactly this.
Have Imprisoned Observer destroy EVERY enemy minion it saw when entering play.
EVERY can mean One. Play Observer on curve when your opponent has 1-2 low health minions, let them live for long enough that they'll be alive when Observer awakens, and ensure they aren't buffed out of range or traded off.
Rush and Windfury granting cards like Animated Broomstick or Battleground Battlemaster can allow you to get this in fewer turns, giving your opponent less time to destroy it. You can also consider doing it all in one turn with a Whirlwind Tempest plus the aforementioned two cards, but seeing how difficult it can be to kill Akama Prime and how much mana cheat is required to make that work, letting it stick a turn should be doable.
Gigantotem which was buffed by Lor'themar Theron becomes a 16/16, plus with Totemic Reflection's buff you're just 2 attack away. Add a Totemic Surge or second Reflection and you can get a 20/20 Totem.
Put an Elekk in a Rogue deck with a ton of cheap/cycle spells.
Draw 10 Soul Fragments in one turn.
Empty your deck, then play 5 of any Soul Fragment generators. Spirit Jailer, Soul Shear, and Luckysoul Hoarder can do this. Be careful about Luckysoul's Battlecry though, make sure to play it last.
Add 7 copies of the same minion to your hand with a single Potion of Illusion.
[MagicKnight] Play an Elemental Mage deck, and get your Overflow Surger to the point where it summons 7 copies of itself. Turn of, play Surger into Potion of Illusion.
Give Speaker Gidra +10/+10 with her Spellburst effect.
Basically, summon 2 Beasts whose base Cost is (6) or more using Guardian Animals. This is done by discounting minions in your deck - Ensmallen in a deck with the cheapest Beasts being 6 mana. Alternatively, completing Jungle Giants and let Barnabus reduce the cost of your Beasts to 0.
Using Steeldancer, summon a minion with the same stats as your weapon.
This one is pure luck, but it can be rigged a bit by picking a common stat total like 3/3 and repeatedly bouncing your Steeldancer with cards like Shadowstep or Breakdance.
This one is just... wacky. Okay, so play Audio Amplifier. Now play Cavalry Horn and use Ebon Dragonsmith 2x to reduce your Ceremonial Maul to 0. You want the lowest cost minion in your hand to be Nerubian Unraveler and a 9-cost spell (your choice of Libram of Hope or Front Lines). On the turn of the combo, you break your Horn, summoning Nerubian Unraveler. You equip the free Maul, and then play your 9+2 mana spell, completing the achievement.
I'm not sure about Jade Idol for the 30 health challenge, primarily because that requires you to get to 30/30 Jades, which most players will concede well before that happens. My best guess is to double the stats on Walking Mountain with Therazane then do Conductivity --> Criminal Lineup to fill your board with 8/32 Walking Mountains, but that is absurdly expensive (19 mana in Shaman) and I feel like there's got to be a better way.
I'll add the Clefthoof one though. You can do it with Baleful Banker with Amplifier and a single Thaurissan discount.
They added a bunch of new Achievements themed around the older expansions with the most recent update. And they're some pretty neat little puzzles to solve them instead of the regular "Play 1,000 Dead Seagulls" so many of the newer achievements become. So I'll list them all here, as well as some solutions to achieve them. If you have other potential solutions, as well as solutions for any I didn't find one for, feel free to comment below.
Note: Many of these combos require more than 10 mana. However, these are all Wild-exclusive achievements, and as such, there's a lot of Wild exclusive mana cheat/ramp effects we can use to make them easier. Even if they don't need it per se, cards like Emperor Thaurissan or Wildheart Guff will make this process much easier.
Rise of Shadows:
Cast Plot Twist and end up with twice as many cards as you started with.
Destroy 6 minions with a single Daring Escape.
Summon 10 Treants with The Forest's Aid in one turn.
Attack with a single Whirlwind Tempest 4 times in one turn.
Add 10 spells to your hand with a single Mana Cyclone's Battlecry.
End your turn with 4 different versions of Dr. Boom in play.
Have a friendly 0-Cost minion in a Duel! and survive.
Summon 60 Mana worth of minions with a single Mass Resurrection.
Summon a chain of 4 Oblivitrons off of another Obvlivitron's Deathrattle.
Deal 100 damage with a single Hagatha's Scheme.
Saviors of Uldum
Cast BEEEES!!! without any of the Bees attacking.
Summon 7 of the same Murloc with a single Tip the Scales.
Complete Hack the System on the same turn it was played.
Destroy both heroes at the same time with Riftcleaver.
Summon 30 Locusts in one game.
Attack the enemy hero with Highkeeper Ra.
End your turn with 7 minions that each have 30-Health or more.
Destroy exactly 5, then exactly 2 minions with a single Earthquake.
Win a game after casting 4 Puzzle Box of Yogg-Saron.
Play 8 Combo cards created by Whirlkick Master in one turn.
Descent of Dragons
End your turn with 6 of Chenvaala's Snow Elementals in play.
Draw a Dragon while not holding one with Breath of Dreams 2 times in one game.
Guess correctly with Envoy of Lazul 3 times in one game.
Destroy the enemy hero with one of Nithogg's Storm Eggs.
End 4 consecutive turns with MORE than 10 cards in hand as a Warlock.
Have Deathwing, Mad Aspect survive his Battlecry at exactly 1 health.
Have the minion summoned by Sanctuary take no damage for a turn.
Win a game after summoning 8 or more Dread Ravens.
Summon 12 Waxadreds in one game.
Complete Clear the Way with the 4/4 Gryphon summoned by it.
Ashes of Outland
Draw (but don't discard) 3 cards that aren't spells with a single Fungal Fortunes.
Cast 6 Renews in a single turn.
Have Warmaul Challenger survive a battle to death with a poisonous minion.
Deal exactly 1024 damage to a Mo'arg Artificer.
Spend 8 Mana in a single turn before your 5th turn as a Warlock.
Have Imprisoned Observer destroy EVERY enemy minion it saw when entering play.
Attack 3 times with the same Akama Prime.
Cast 10 Libram of Wisdoms on the same minion.
End 8 consecutive turns while in Metamorphosis.
Draw a Clefthoof with Scavenger's Ingenuity.
Summon a 20-Attack Totem with Totemic Reflection .
Scholomance Academy
Teach a single Educated Elekk 15 different spells.
Draw 10 Soul Fragments in one turn.
Add 7 copies of the same minion to your hand with a single Potion of Illusion.
Give Speaker Gidra +10/+10 with her Spellburst effect.
Summon two Beasts that cost (5) or MORE with Guardian Animals.
Using Steeldancer, summon a minion with the same stats as your weapon.
Destroy a Failed Student with Disciplinarian Gandling.
Deal 10 damage at once with Ras Frostwhisper.
Have High Abbess Alura cast the Legendary spell that triggered her Spellburst.
Summon a Blood Herald with 30 or more Attack.
Summon an 11/11 Student with Ceremonial Maul.