Updated Februari 2021

Game Plan

In the early game, fight for the board using the hate minions. There are 7 in the deck and you can clone them with Felosophy and draw more using the hero power and Free Admission, so you should be able to deal with most boards. Dragonslayer is the least efficient of the hate minions, so try to use her before the others.

If an opponent goes wide with for example Mechwarper, you have Defile to clean up the board. You can use Nether Breath and Demonfire to deal some damage to individual minions when there are gaps in the sequence. In case of emergency, the 1/1s from a discounted Leeroy Jenkins can be used to complete a Defile setup.

Because most opponents will have at least some of the hate minions as well, there is a crab-eat-crab meta where you are at a disadvantage if you play your hate minions first. So if the board is not threatening, draw cards and look for a Defile opportunity instead. Ideally you'll have the last move in the hate minions ping-pong by having a Dragonmaw Poacher survive.

In the mid-game, after you played out your hate minions, use Voidcaller and Skull of the Man'ari to summon chargers and taunts for free. Try to push a bit of face damage when you can, but don't take too much risk leaving minions on the board. If anything good survives a turn or an expensive minion is pulled from your hand, Ectomancy is a good way to cash in on that.

If you win the board or the opponent runs out of cards, the mid-game is where it ends. Otherwise, tap for Bloodreaver Gul'dan. Heal with Nether Breath and Zilliax when there are good opportunities, to make sure you are still alive by turn 10 to play the Death Knight.

Replacements

You could replace Old Murk-Eye or Leeroy Jenkins with Reckless Rocketeer. For Charged Devilsaur it might be better to substitute something with good stats rather than a charger. For example Enhanced Dreadlord could be an option.

Alternatives for Felosophy and Hungry Crab would be a second Dragonslayer and Soul Shear, although the latter is not ideal since you'll be facing a lot of 4-health minions (buffed Crabs and Crawlers).

Skull of the Man'ari doesn't have a good replacement but I think the card not essential, since you still have Voidcaller to fall back upon.

Bloodreaver Gul'dan could be replaced by N'Zoth, God of the Deep. Another option would be to use Envoy Rustwix to give your deck more staying power.

Zilliax could be replaced by Man'ari Mosher or a rush minion like Scaleworm or Ruststeed Raider.

I don't think there is a direct replacement for Ectomancy: for example Faceless Manipulator can do the cloning, but since it's a minion it might get pulled by Skull/Voidcaller. It's a situational card though: not essential for the deck to function.