Hearthpwn

Make sure to use every opportunity to heal Valithria Dreamwalker to 5 and attack Lady Deathwhisper. These opportunities are:

• Circle of Healing
• Voodoo Doctor together with hero power Lesser Heal (Requires 3 mana!)
• Squashling together with hero power Lesser Heal (Requires 4 mana!)
• Holy Nova together with hero power Lesser Heal (Requires 7 mana!)

Always keep these cards for healing Valithria Dreamwalker. All of them, except Circle of Healing, should be played together with your hero power in the same turn to get Valithria Dreamwalker to 5 health and attack. So check you mana before playing one of these cards. ;-)

Mulligan

Always try to start with one or two Circle of Healing. That way you can start attacking right away.

Board control

Use the spells and minions with silence (there are plenty in the deck) to get rid of taunt minions. And standard Priest spells like Shadow Word: Pain and Shadow Word: Death to kill them.

Good luck

You do need a little luck with your draws, because you won't be able to control the board for too many rounds. But you should be able to get the kill within a few tries.