Hearthpwn

It might sound weird if you have never seen this concept before, but this is a really powerful deck that has more win conditions than just milling.

Deck Intro: 

There's 2 main ways to win with this deck: Milling and Control and it excell at either of them depending if you know your opponent. So stay chill and observe them and commit to either one around turn 6-8 to win.

Mulligan:

Never keep 5-mana cost cards and up in your mulligan as it's crucial that you hoard Urchin Spines to combo with Grievous Bite or Bola Shot against at least 3 big threats at a time (or less if you really are desperate) during mid game before you get access to Imported Tarantula revival that give you all the removal with deathrattle triggering cards you need against late game threats.

Another cards that should never be kept are Nine Lives , Revive Pet and Yelling Yodeler as none of them help you at all before you have played a Deathrattle minion first.

Gameplay:

Turn 1 always play Flare unless you know your opponent plays Secrets, then keep it for those. It's also the tech card so can freely change it to something else.

If by some chance Imported Tarantula gets in your turn 1 hand, it's preferable to trade it here if you have no Flare.

On turn 2 if have no 2-mana minions and only Monkeys, but know that your enemy minions don't exist or won't be instant threat to you, you can just hero power with no care on this turn and wait for better opportunity to Bola or Bite more minions. (The Monkeys damage is peanuts so they aren't worth it for damage in comparison to what your other minions or fatigue does).

On turn 3 you should almost always play Prince Renathal and only play Coldlight Oracle here if you have Far Watch Post on board or absolutely know that enemy can't turn the drawn cards instantly against you. 

On turn 4 Selfish Shellfish is a good card to play since its such a stat monster, but if want to coin Pet Collector here it is the most optimal play since it might give you a "free" Shellfish. Necromechanic is not a bad card to play either, but it's not optimal here and is often better used later. 

On turn 5 you need to start pay close attention to enemy board, hand size and the possible cards they will play if you already haven't. Especially if you don't have any Imported Tarantula or Urchin Spines in your hand as you can't deal with multiple future big threats without them and have to trade your board for them and that is not good for this deck at all.

The ideal card to play on turn 5 is almost always Pet Collector, but depending on the situation here's where the deck starts to go off auto pilot and turns fun. As you have to start figuring out your win condition here. If you still have the coin you can use it for Mister Mukla for instant board presence that hardly ever gets taken out next turn and solidify your mill strategy even against aggro since it fills their hand. The possibilities are endless this turn, even with bad cards.

On turn 6 keep doing same thing, but start to commit to your win condition. UNLESS you still have the coin, then always use Guardian Animals as this deck has limited beast minions so it's best to use both copies as early as possible - this also flips the board in your favor almost always.

On turn 7 do the same unless you ran out beasts in your deck. At this point forward you should be repeatably using your deathrattle triggering cards and Revive Pet to either win by control from Imported Tarantula minions or mill 8 cards a turn to get opponent to early death or in rare cases defend with so many Teacher's Pet that enemy aggro crumbles. There's also some games where I have won with just face damage, but don't count on that. Then there's the secret wincondition with half assed millling: Keymaster Alabaster that allows you to fill your hand with 1-mana cards you drew for your opponent to get new winconditions.

I haven't faced a deck that plays little to no minions yet, such as Quest Hunter, but I can tell this deck can't beat them since this deck is all about control and has no healing capacity at all.