The battle against Lady Deathwhisper is a frustrating one without the right cards in your deck.
She reduces the health of your minions to 1 each turn, and unless you heal the 30/5 minion on your side of the board you can’t attack with it.
This is how to beat Lady Deathwhisper with a really cheap Priest deck containing mostly basic cards, so anyone can build the deck and complete this mission quickly.
Decklist to Beat Lady Deathwhisper
Video: How to Beat Lady Deathwhisper
Here are guides to the other bosses in The Lower Citadel: