This deck is for trying to finish quest on turn 9 or earlier. That is why it is fast.
Always keep the quest. You have so many taunts and board clears that you will get them against aggro for sure and then finisht the quest and just finish them off with 8 damage hero power.
Also keep any 3 mana taunts if you expect slower deck, keep all board clears up to 5 mana if you expect possibility of aggro (yes keep Brawl, as it is the most reliable sometimes, you might have problems playing some of the others before turn 6 sometimes)
Against Druid keep Cornered Sentry, don't play it though early because if it is Token Druid you can be punished, play it as soon as you are certain he is Taunt Druid though.
Some general suggestions on strategies
Try not to use board clears early... 3-4 small minions can just be ignored for a better board clear next turn.
Keep Phantom Militia for 6 mana or 9 mana turns to finish of quest (play it on 6 mana only if you have enough other taunts to finish the quest) Still keep militia in muligan though against slower decks, as it can be emergency taunt, but otherwise they are very important for finishing quest.
You do get Sulfuras early sometimes, but playing it right away might be certain death against aggro and midrange decks sometimes. Stabilize first and only then play it, or play it if it is your only way to survive (like you need to kill priority target with the weapon or fireballing some huge guy is the only way to remove lethal from your opponent)
Keep in mind that you can do armor up + sulfuras + die insect and have 3 mana leftover to do something else. Or sulfuras + die insect and have 5 mana leftover. If you don't plan to use Die Insect hero power better not play sulfuras at all (with rare exceptions when 4 damage is just what you need and there is no other way of doing it)
Cornered Sentry is Witching Hour counter but can be used easily in any other match up. Against control you can play her whenever board is empty especially if it is early in the game, they most likely will just trade raptors in and you will have a 2/3. Otherwise especially against aggro and midrange play her right before board clear if you have 2 extra mana available. (if it is Warpath play her right before last time you warpath to end up with a 2/5 taunt)
Below is a good game replay against even shaman which demonstrates most of this. On turn 5 it shows an efficient way of getting rid of early huge minion together with all the board and the whole reason Reckless Flurry plus Drywhisker Armorer are in the deck. I had a brawl since beggining but used it on turn 8 when board actually became threatening. Used militia as an emergency triple taunt very late.
I finished quest on turn 10 (which is slightly later than optimal, but mostly because I had to board clear twice) Even though there was scary buffed Al'Akir on board for couple of turns I still kept Sulfuras in hand and tried to stay alive with different means, until my opponent actually went all in and emptied his had, at which point I could play Sulfuras while also playing Tar Creeper and double hero power and leaving my opponent with just one minion, a 4/8 but still can't connect face.
Cornered Sentry and Acolyte of Pain are tech choices in current version of deck. One of them can be replaced with weapon removal of your choice if you encounter some scary weapons, but after nerfs it seems to not be very often, and Vinecleaver for example is countered by board clears so you don't even need to bother with it.
The Lich King can be easily replaced because he is not very good in the deck to begin with. Options would be mostly cheaper taunts like second Cornered Sentry or maybe Witchwood Grizzly if you face a lot of aggro.
Here is Kripp playing my deck. He is pretty good at piloting it (somewhere in the stream he says that it is me that suggested it)
Updated to a better version that Kripp came up with on second day of playing. Witchwood Grizzly was only strong in match ups where deck is strong anyway. So weapon destruction and card draw were teched in.
Here is some gameplay:
Replaced Ooze with a copy of Cornered Sentry as there are not many weapons that you would remove after nerfs it seems. Weapon removal is not needed until Cubelock comes back (if it ever comes back at all)