This deck was made specifically to defeat Heigan the Unclean Heroic. As a cheaper and more consistent alternative to the suggested Miracle Rogue.
NOTE: This deck is slow-paced but very solid. Expect to go past turn 10 and don't worry about taking damage early as this deck provides a LOT of healing. Allow him time to use his Demonfire to buff before using your clearing spells!
Other minion cards are purely fillers, ones that either won't be 1hit by the passive Sen'jin Shieldmasta and cards that will benefit from it Nerubian Egg & Haunted Creeper. Once you have the Stoneskin Gargoyle down, you should aim at dropping the Sunwalkers which he will attack and clear his board, finish the rest off with spells while hitting him directly with everything else.
I threw a mind control tech in there which will help if the board is getting too full and is a great help to swing it back in your favor.
Mulligan: Soulfire, Sacrificial Pact, Nerubian Egg, Stoneskin Gargoyle. Don't just throw them out though, the Stoneskin Gargoyle you should mulligan for but save it until he has used his clearing spells (Shadow Bolt ect.) on other minions. As it stops a lot of pressure from his passive.
Thank you all for your feedback and input. I'm glad my deck helped you defeat Heigan (Or helped you build a deck that did) and thank you for the support! I'll no longer be responding to comments, but hope this continues to help others that get stuck. <3
Here's a couple of videos of other users using this deck.
Thanks to MattSparks!