This was probably the best/fastest climb to legend I've had since I started playing HS in 2014.

I had a 64% WR climbing from Diamond to Legend. I had multiple games that I won in the 1st 4 turns. This deck wins fast and loses fast and, if you're looking to climb fast,  you shouldn't be afraid to conceded a game that's most likely a loss at the earliest possible moment to move on to the next one. 

On Mulligan you are looking for your premium 1 drops (Tunnel Trogg, Surging Tempest, Intrepid Initiate) and your turn 2 follow up (Totem Golem, Cagematch Custodian). Managing your overload is important early and planning out your available mana for max damage every turn. 

Some good early mini-combos I used to great effect are Trogg/Tempest into Golem, Initiate into Trogg/Tempest w/Storm's Wrath. Often on turn 3 I was playing either a Whack-a-Gnoll Hammer, a Wriggling Horror w/a 1 drop or a Diligent Notetaker and a 1 mana spell. 

Force your opponent to trade into your minions (if you are trading into theirs somethings going horribly wrong) and only use your burn/weapon as minion removal when absolutely necessary (every point of damage to face if possible). Every turn you should be doing the lethal math looking to end the match as quickly as possible.   

I found that opponents tend to mulligan incorrectly against this deck as they are expecting Evolve Shaman or Big Shaman. I took advantage of this and applied max pressure early even to the point of over committing to the board. Against heavy control decks especially if you don't win early you won't win so there's usually no reason to hold back. 

This deck can easily be made budget by replacing the Vessina and/or the Doomhammer with Bloodlust. Other (non-budget) options are Sea Giant, Inara Stormcrash and Leeroy Jenkins.

PS: The Devolve was added specifically to deal with large taunts or buffed minions. It's great against decks like Big Priest, Odd Paladin or Aggro Druid.