Don't forget that you don't have to get 78 coins in a row to get the hard badge. Having a high multiplier helps, but continuing the game even after losing the multiplier can still net you the 100,000.
Don't give up.
@Admiral Zetsu Talk to the alchemist again, he'll make it for you. Tonics in the bar, crickets under the bed, mushroom is in the bushes in the front of the house.