Doom Lord Kazzak is quite an easy encounter for a "challenge mode".

His passive hero power, Twisted Reflection, heals him for 5 every time one of your minions die. I took this as a sign that I shouldn't play anything aggressive since he likely has ways to defeat really small minions and oh yes, he does. I took a guess that a no minion mage deck would work well and well since I'm posting about it, you can only assume that this was a great call.

The deck isn't exactly cheap, but I do feel if you've been playing mage over the past couple of years, there's a good chance you're already going to have some of these cards. For adventures specifically, I've always had the thought that there is not only one correct solution for the problem anyway, especially if you can make it fun, and I love me some no minion mage.

Defeating Kazzak

Keep your quest.

Mulligan for Incanter's Flow. While not required to win, one (or two in one game of mine) of these goes a long way in cheating the battle since we have so many high-cost spells. If you have Learn Draconic in your opening hand, you should opt to keep it.

We're going to play a control early-game, trying to avoid damage where possible. We're not going to worry too much if we take damage though since we outperform his slower-paced deck with ease, taking control of the situation and getting to choose when he heals (if at all). 

One huge benefit we have is that Kazzak plays several minions which have lower health numbers and it isn't unusual to see 3-5 of them on the board at the same time. They can be taken out easily through Blizzard and Rolling Fireball, which are easily accessible options in the mid-game, even without discounting their cost.

Your Important Tools

Save Polymorph for Enhanced Dreadlord. The card is incredibly annoying since the 7 health alone can be hard to overcome but also the spawned Lifesteal minion just ain't cool. Don't give him more opportunities to gain life!

Apexis Blast should be used when you're starting to establish your board. It easily helps complete Learn Draconic which will further build the board and force Kazzak into hiding. After those beefy minions are out there, keep control.

If you run into problems, Puzzle Box of Yogg-Saron is here. I've never needed to play it, so use it for a killing blow on this jerk of a demon.

Evocation is much like Puzzle Box. I haven't needed it, but it is a very easy way to get control of a situation that has somehow not gone too well.

Kazzak's Annoyances

Chaos Gazer is a nasty card but ultimately doesn't do much damage because our superior spell generation will save the day. It remains a sad time though when it forces us to make the "incorrect" move if we really want to use the card.

Terrorguard Escapee is present in Kazzak's deck. There isn't much you can do to counter it other than having a full board or getting some RNG on your side which gives you large taunt minions. Don't worry too much about it, it's okay if Kazzak gets to heal a little bit.

Rustsworn Champion is an adventure-specific card that is an unfortunate reality. Not only does it force us to play a card or lose it like Chaos Gazer, but it also has Charge meaning he will almost without a doubt be healing.

Hellfire has the highest chance of healing him back up, but I haven't encountered this actually being a problem. It can make things feel sketchy though!

Card Replacements

Like I said, the deck is expensive and that definitely doesn't work for everyone. If you want a more budget-friendly approach here's what I'd recommend changing.

Remove both Puzzle Box of Yogg-Saron. I never actually needed to use it and the inconsistency can be a negative in an adventure. I'd sub in two Frostbolt since they work well to establish your early-game dominance and can be used just purely as control later on if needed. 

Remove Evocation. I love the card to death and it can pull you back into the game if something goes wrong, but honestly, this fight is so easy I don't see it being needed. Adding a second Magic Trick can help you choose the correct tool for the situation.  If you don't have a second Magic Trick to bring to the table, a second Tome of Intellect can get you similar results, just hope Yogg's luck is on your side.

Rolling Fireball is a very good card since it helps remove even Kazzak's higher health minions, but if you aren't one that has them available, a couple of Flamestrike will help you out with the second good part of Rolling Fireball which can be used as a mass board clear.

I wouldn't recommend any other replacements. The only remaining higher-cost cards are Raid the Sky Temple which is one of the more important parts of the deck with its insane spell generation, and Power of Creation which actually helps is establish minions on the field. You could sub in regular Fireball for Power of Creation, which would help with control or just direct face damage, but you'd be relying on RNG minion generation only.

Here is a link to the more budget-friendly build.

Ultimately, this is the opposite of a difficult fight and I feel this deck, even with substitutions, will drop Kazzak off the face of Outland. Thanks for coming to my TED Talk.