Mulligans
The plan is simple :
Draw your whole deck using Starving Buzzard and your cheap beasts.
Use Dreadscale + Serpentbloom, Reno Jackson and Zephrys the Great to stall the game and survive (or clean your own board for Mecha’Thun activation).
Get Flark's Boom-Zooka, Mecha'thun and Sir Finley, Sea Guide as the only cards in your hand (you can still do this with up to 2 other minions) . Then your winning combo is :
– Play Finley to put your hand in your deck. If you still had some cards there you will need to play them this turn.
– If the next card you’re about to draw isn’t the Boom-Zooka (check the card order, the leftmost card in your hand becomes the top card of your deck), attack with your equipped Harpoon Gun to dredge it.
– Wait until next turn to kill your board, play the Boom-Zooka and detonate your Mecha’Thun.
Congratulations, you won !