As RNG as the boss is they are a couple of ways to deal extra damage. The general strategy is to hope for the attack when the boss summons the woolies with lightning as it sometimes allows you to hit the boss multiple times.

You usually want to run into something that will kill you when the boss drops the wool from the sky.

There are three ways I know to hit the boss when you're not supposed to be able to.

1. Breaking the shirt's shield and then going back inside the boss and jumping
2. Jumping into the boss when it does the charge attack towards you (This can frequently kill you)
3. Hitting the boss after it finishes the laser attacks, going above it and jumping on it as it rises before the shield comes back

Video example: