This Corrupt the Waters deck is based on current existing versions of Shudderwock Shaman, which has been able to reach high legend in the hands of skilled players.
Early lackey generating cards are used to complete the quest and control the board in the early game. Zap! and Voltaic Burst can also be used to remove early threats. Try to play Questing Adventurer as soon as possible, since it becomes an ordinary 2/3 after the quest is complete.
In the mid game, Thunderhead and Vessina are persistent threats that bring extra value to your overload cards. Weaponized Wasp is efficient removal in this part of the game, and Mind Control Tech can swing the board if things get out of control. Former Champ or Giggling Inventor followed up with Mutate can be a powerful tempo swing.
After quest completion, your hero power has 3 main purposes; generating cards, building your board, and burning out your opponent.
The improved hero power significantly improves your ability to generate cards. Sludge Slurper and EVIL Cable Rat will generate two lackeys, and if you're lucky enough to generate Ethereal Lackeys, those will generate two spells each. Swampqueen Hagatha will generate two Duskvarr Horrors, which can have their battlecries doubled as well, potentially generating more cards. Shudderwock can't have its battlecry doubled due to the mana cost, but it can generate several lackeys, a Duskvarr Horror, and random spells.
By building up your board with little card investment you may be able to outvalue most opponents and stick a sizable board. Your lackey generators allow you to quickly fill the board with cheap minions. Giggling Inventor creates a wall that your opponent will have significant trouble breaching. Former Champ simply puts a large amount of stats in play across several bodies. Shudderwock will do both. You can follow this up with The Storm Bringer, Vessina, or even a Bloodlust generated through a spell lackey or Swampqueen Hagatha.
The hero power also gives you the option to burn your opponent's face to the ground. Lifedrinker will deal 6 damage and heal you that much. A Kobold Lackey followed by a Weaponized Wasp is a 6 mana Pyroblast! Shudderwock has a large damage potential, but keep in mind the Kobold and Wasp battlecries can hit any target, including your hero and minions.
Other Cards for Consideration:
Bloodlust - Swap for Vessina. I opted for Vessina over Bloodlust because I believe this deck generates enough value that a Bloodlust finisher is unnecessary. Vessina is a much more versatile card, and can be played on curve as a threat. This deck also has a high potential for generating Bloodlust between spell lackeys, Swampqueen Hagatha, and Shudderwock.
Likkim - I really wanted to include Likkim in this list but I just didn't have the room. There are enough overload cards for Likkim to be consistent, and I have found Likkim to be a powerful card for early board control. Likkim should definitely be slotted in if early game board control becomes an issue for this list.
Underbelly Angler - Underbelly is a powerful value generating card and persistent threat. Current Shudderwock decks run it, but I feel that the value lost by excluding it is more than made up for by the quest reward, and running cards that synergize with the reward is worth more than the randomly generated murlocs, and the necessary inclusion of Murloc Tastyfin. In my experience however Underbelly Angler has been an extremely powerful card in a variety of situations, so it should be experimented with in this deck.
Siamat - Personally, I'm not very excited by this card. I think Walking Fountain is better in almost every way. People seem to think it's the next Zilliax, though, and it has synergy with the quest, so it should definitely be tried out. Perhaps a more elemental focused variant of this deck, with Menacing Nimbus and Earthen Might could be tried.
EVIL Totem - Depending on the early minions and removal available, EVIL Totem may need to be swapped out for a different minion. I included it due to the threat it poses of generating large amounts of value, and because it makes the Weaponized Wasp more consistent.
Questing Explorer - While this is a powerful card while the quest is up, the Shaman quest can be completed fairly quickly, after which this becomes a simple 2 mana 2/3. While the value generation of the quest may be enough to outweigh the value of drawing cards, it's possible that a repeatable draw may be better for the deck.
Zap! - Zap is a great removal tool, and it combines very well with Thunderhead. It may be too weak on its own however, especially without Likkim in the deck. A higher impact overload card may be substituted for it.