There was a guy in my country (Brazil) who finished cuphead without using the shots. He used the ax to attack and the specials. Even in planes he didn't shoot, but rather used the ax and turned himself into a bomb (the special one, not the normal "shot" bombs; the challenge was not to shoot, but turning into a bomb isn't shooting).
It took him almost 100 days and sometimes he died more than 200 times in a boss, since the only way to cause consistent damage was that ax relic, but it took dozens of attacks of that to pass a boss phase, not kill the boss . There were bosses that needed dozens of axes.
In the last phase of the robot boss (when he uses the diamonds to attack everywhere), because of these constant attacks, the guy had to wait for the entire attack to finish, go to the boss, and do an ax attack. And then he had to go back, because the boss would attack again in the area with the diamonds.
It took 100 attacks with the ax for the boss to die, so he had to survive 100 cycles of attacks from the boss.