So, Shimmering Cave and Dark Forest what I can tell you about for now.
For both challenges the HP of the bosses got highly incrised (to ca. 100).
They have more cards, so any kind of rush against them is impossible, and decks of 25 cards or more is a demand.
The decks of the AI seems to grow more specific. Less random archer in it, the Shimmering Cave is almost entirely made of Goblins, and Dark Forest made of Dogs and Lizards and elf snipers. This means you better design your deck to be able to handle that specific area (although your normal strong deck will probably be enough, so do not overdo it).
A hint: if your deck lacks elemental damage, but is solid otherwise, put in a couple (5+) Undead. They are easy source of elemental damage, and will likely come back to your hands from the field, incrising their usefullness even further.
The AI will without doubt be able to constantly cast Skill-cards (aka. spells), so don't expect just sacrifising some monsters at the beggining of the battle will save you equally effective as on Normal difficulty.
The HP/Attack scores of things also got incrised for this difficulty, not to mention the Barrells at Shimmering Cave deal more damage (so what stands right at them when they are destroyed, will most likely die from your creatures). The enemy groups also got more of the special monsters.
The prime reason to beat these levels over and over again is Tier 3 equipment, what currently is best in the gaer as far as I know (King's set). Shimmering Cave has the Helm, Forest has the Cape).