At @Vocino request here a guide on how you to can get Arthus in Hearthstone.
To get Arthus you need to beat the Lich King with all 9 classes, the catch is that the Lich King cheats by using a spell the first turn to hamper your deck. But you do have one advantage you have the ability to change your deck in both standard and wild to abuse his trick right back at him so I present you the ways you can beat him both the easiest and cheapest ways possible.
Challenge - Destroys all enemy minions that cost 3 or less
This one is the easiest if you ask me, you know why Jade. All you need is control cards to keep him in line as you amass you Jade Golem army. Best part being Jade is rather easy to make as you don’t need that much dust to get the cheap ones. Get Jade Idol, Jade Spirit, and Jade Behemoth all of which are common cards and focus on staying alive through spells early and drawing cards. You can also refine this by reducing the cards in deck by purposely putting 3 cost minions to be destroyed.
Challenge - deal 2 damage to your yourself for each minion in your deck
You got a few ways to do this, cheapest is using either Scavenging Hyena with spells summon minions to buff or build a deck with 14 minions to reduce you health off his spell to turn 2 drop 2 Molten Giants to destroy by turn 7.
Another easy but expensive way is to play meta spell hunter with the possible void ripper and explosive trap setup
Challenge - Your remaining health is set to 1
Honestly just do the molten giant combo and use cards that copy minion to finish him off
Challenge - whenever your minions dies, he takes control of it
See my video guide here for you cheapest option
Other than that Beardo Deathknight combo also works
Challenge - You can’t emote
Easiest curse, most priest standard deck can beat him easy, throw cards like shadow word horror to clear the 2nd part. For suggestions for cheap decks Test Subject OTK and Silence Priest are decently cheap and are fine in standard
Challenge - All spells are destroyed
This one might be the most costly to beat. Easiest is Quest Rouge and it honestly probably the least frustrating, so save your dust.
Challenge - All your minions are set to 1/1s
Shaman a bit tricky, off the top of my head Shudderwock could work (not tested since I dropped hearthstone) but that deck is costly. Cheap wise token evolve shaman can get you results and card like nerubian egg and devisaur egg can as well get you some good damage as they can easily pop their deathrattles.
Challenge - 2 damage for each duplicate minion
You could play Renolock or Demon Deathknight Warlock or alternatively just do the Molten Giant combo with murlocs and purposely put in duplicates.
Challenge - Lich King starts with 100 Armor
This is another costly one, the best decks for this are Deadman hand Warrior and Grim Patron Warrior but will take some work to learn how to pilot if you even get the cards so be prepared to restart a lot.
That is how you can easily beat each challenge, hopefully this will assist. If you need assistance feel free to message me as even though I no longer play the game I know a thing or two about the game and resource to help players with this task.