So I started playing this deck a couple of days before the 19.2.1 patch (Edwin and Boggspine Knuckles nerf). I was doing quite well from the beginning, but especially post-patch the deck is insane. My current record is 25-6, including a 13-1 run from diamond 4 to legend (I was 10-0 and then lost to a Maly Druid).
Key cards are:
Lightning Bloom: allows you to cheat out your Guardian Animals way too early
Animated Broomstick: allows you to play one of your beasts from hand and either draw 2 or cleave and clear 3 enemy minions
Overgrowth: No explanation required
Strongman: The fact that Guardian Animals can corrupt this and make it 0-mana makes your big turn even more swingy. Frankly, the nerf to Guardian Animals from 7- to 8-mana probably helps this deck. It is also nice to have something to play for free on the turn when you spend 10 mana for Survival of the Fittest
Guardian Animals: No explanation required
Ysera, Unleashed & Carnival Clown: These are late-game win conditions against slower, control decks
The deck is optimized in terms of ramp & mana cheat and some card draw so that you can get to your big turns as fast as possible. It only runs 1 copy of Overflow as it is often quite expensive and/or clanky in a relatively full hand (which happens often as Twilight Runner can often draw you cards over multiple turns). I replaced the 2nd copy with a copy of Guess the Weight, for some early game card draw. I also run one copy of Crystal Power for either some cheap removal or some healing in order to stay alive until the big swing turn. These last 2 cards are kind of optional and can be replaced if for example the meta requires specific tech cards.
Y'Shaarj the Defiler: Greedy, win-more card. If you have already corrupted and played a Carnival Clown, you will probably win anyway and if not, he is just too expensive and not swingy enough.
Yogg Sharon, Master of Fate: Not only does the deck run too many minions for Yogg to be consistently active, but he is also not a good card overall. Sometimes he can help you come back from games where you are behind, but if you have reached 10 mana and you are still alive then you are almost always ahead, in which case you probably don't want to play Yogg.
Always keep: Nature Studies, Wild Growth, Overgrowth, irrespective of matchup. Guardian Animals is also a keep almost always as this is the spell that you want to cheat out as early as possible. Lightning Bloom is also a fine keep most of the times, especially if you already have ramp and/or Guardian Animals in your mulligan. I rarely keep Innervate (unless I already have Overgrowth & Guardian Animals as it is not as high-impact). Once, facing a Rogue and having already Overgrowth in my started hand, I kept Lake Thrasher and Animated Broomstick, but the scenarios where such a mulligan makes sense are very rare.
Aggro (whether Demon Hunter, Hunter, Rogue, Shaman or Zoolock): These matchups are always a race. You will take a lot of beating in the first few turns, but if you manage to draw your ramp into Guardian Animals and ideally cheat out a Strongman or an Anubisath Defender with it, it will often be too much for them to handle. Against Hunter exercise some care when playing around their secrets (e.g. Coin out an Animated Broomstick to proc Freezing Trap, consider board positioning for how Pack Tactics procs before attacking with Lake Thrasher). Hunters and Rogues have some burn from hand via spells which means you are never safe while on low health, even if you drop big taunts. I'd say most of those matchups are round 50-50.
Evolve Shaman: This deck was horrible to face pre-nerf. However after the nerf (a): they are almost nowhere to be seen and (b): the deck lost quite a bit of its power level by not being able to cheat out the 3/3 pirates for free, thus delaying their swing turns. I guess what was pre-nerf a very tough matchup for us is now probably around 50-50, but shouldn't matter too much as that deck dipped a lot in popularity.
Paladin: Pure Paladin should be a very winnable matchup, as their only board clear is an expensive 2-card combo (Libram of Justice into Concecration. Libroom Paladin also has Lord Barov + Animated Broomstick, but our deck can in general create more boards than they can clear, so once again you should be favored
Priest: Priests have access to (or can discover) quite a few board clears and therefore you should exercise some care not to overextend. Instead keep creating threats via medium-sized boards to bait out their removals and finish them off with either corrupted Carnival Clowns or a board of Ysera dragons. When playing Carnival Clown keep in mind that, apart from Soul Mirror, Murozond the Infinite is also a strong answer, so make sure you have some reply to such a play (e.g. the 2nd copy of Survival of the Fittest). Some resource management is important, but overall this deck should destroy Priests (I am 5-0 vs them)>
Warrior: Somehow I've only faced Enrage Warriors which were very easy to beat (as they don't even run Brawl). However for Control Warrior the same thing as above applies: They have access to quite a bit of removal, so stagger your threats and take care not to overextend (and don't play Carnival Clown on a fully empty board to let them die to a single Bladestorm) and the matchup should be very winnable. Haven't faced any Bomb Warriors either, but those might be even tougher as, apart from the removal they run, they can also deal a ton of damage with their bombs as we draw through our entire deck quite fast.
Tickatus Warlock: This matchup should also be good for us. They don't have any other win condition apart from burning our cards and by the time they have drawn and corrupted Tickatus we should already be on 10-mana and have a bunch of big beasts and taunts on the board that they need to answer, thus never getting the chance to play Tickatus. There was one match where I had to use every single resource available to win as the opponent used 2 copies of a fully corrupted Cascading Disaster, 2 copies of Plague of Flames and 2 further copies of Cascading Disasterobtained via [card]Y'Shaarj the Defiler to clear my board 4 times, but eventually they had no answer for the 5th board I created (2x Guardian Animals + free taunts, 2x Carnival Clown and 1x Ysera dragons)
Combo/Secret Rogue: The Edwin nerf made it harder for this deck to high-roll on turns 1, 2 or 3, while our deck can consistently high-roll on turns 4 or 5 making this matchup quite favorable in my opinion. Rogue doesn't have too much access to removal and should normally struggle to deal with our big board created by our swing turns
Mage: I've barely faced any mages. I think the most popular deck is a controlish HL mage. That should be a very good matchup for us as Mage is not that great of a control class in terms of removal. They might manage to clear 1 or 2 boards then freeze and stall a bit, but eventually they should run out of answers
Some general observation: This is a high-roll deck. If you play Nature Studies on t1, Overgrowth on t3 and then Coin + Innervate + Guardian Animals on t4 then you will win 90+% of your matches, no matter what deck you face. If you low-roll and never draw your ramp or your Guardian Animals you will lose to pretty much any deck no matter what. However, with the right mulligan, this deck should manage to draw its key cards more often than not.
Have fun playing it and let me know if you have any feedback!