The deck you get in the Anduin vs Thaddius class challenge is heavily focused on getting board advantage using your healing and health buffing hero power/cards. You can also take control of enemy minions for even more advantage. Timing your minnions attacks when enemy minions have low health/low damage is also important since Thaddius will automatically cast his hero ability each turn.
Primarily use your hero ability on your minions after they have attacked to keep them alive for longer allowing you to take out multiple cards with your one card. Enhance this further by using the health buff cards on minions with roughly the same health and damage so that Thaddius’ hero ability doesn’t make it much easier to kill your buffed minions.
In each of Thaddius’ turns he will cast his hero ability to swap the health and damage of all minions. Hence if you time it right you can take out his minions with low attack minions or keep your minions alive when Thaddius’ minions are high health and low attack.
Also use the many minion stealing cards to take Thaddius’ minions and use them to kill Thaddius’ other minions rather than your own.