Actually Saitama is still in the game. If you get the option to "hit the gym" after finishing a run (which I think is exclusive to completing the game on the hardest difficulty), you can unlock him. Once you're in the gym, you'll know what to do. ;)
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The difficulties are represented by the minimum wage of the company. To increase the minimum wage, beat the final boss and choose to yeet them off the building afterwards - then you'll have the option to increase minimum wage. You only have to do this twice to unlock the hardest difficulty of $25 an hour. (I think you have to beat the game on the second hardest difficulty to unlock the hardest difficulty, although I'm not entirely sure of that.)