The way I did it with Tess was to get spirit lash from the HP and spam that, though it's very hard if she doesn't cast that. Not as harsh as that one that summons 1/3s that hit everything for one on deathrattle when your stuff dies, that is a pain. Of course, you can always go the cheesy routs of Exterminate with cost reductions. That's a fun and easy 28+ damage.
I was super lucky the one time I faced her I was running patron and whirlwind effects so that was easy, but I imagine my strategy otherwise would just be to get +health and heal 2 at end of turn, take control of the board entirely and have some removal ready for the inevitable mass mind control. But sure, if you're sitting with the wrong kit she is probably quite literally impossible.
For the level 7 bosses, sometimes it just comes down to luck with the deck you built. I think each class has a way to answer Azalina, but it's not easy. Shaw obviously has lots of rush power, and Tess has fan of knives + hero power to consistently have one available, Darius has the cannon(s), and Toki has chaos spells like Arcane Missiles.
I’ve been unlucky to face her well over a dozen times between my runs as Tess and Crowley. Finally made a full run through with Tess but I legit got placed against her 6 runs in a row with Crowley and each time got my shit pushed in. Tried different strategies but I can’t pump enough damage or even control out fast enough to prevent the mass mind control or the solid swarm of wisp buffs. Two of the times I died in the first few turns cause of unlucky shuffles but even then, getting wrecked in the first few turns is frustrating when the cards don’t line up. That boss is made of pure bullshit, hate to be that guy and say nerf please but holy...fucking...shit