well, you can get 32 ic without jumping but you have to beat the sun
if ledge climb counts as a jump, we only have to jump once
You only have to press A once to do a ledge climb when you have the flamethrower but you have to press A a bunch of times to beat the sun I don't think the sun or the ledge climb should count because they aren't really jumps and another reason for the ledge climb: you can do it with the X button without any powerups, but since pressing X activates the powerup ability, the only thing that works is pressing A. So, you're doing an action that doesn't have to be done with the A button, but you're doing it with the A button because you can't use another button (the X button)
you do have to press A a couple of times to get up ledges when you have a powerup
I feel proud of myself
here it is:
I found a new way to get to the egg hunt portal in Tinyhuge Bedroom using the fan and it could be useful since it looks faster but I don't know