Story-related, can't be missed.
For this boss, just jump over him until he goes on the ceiling, then he'll throw down some gum minions and you'll need to stomp on them so they don't attack you. He will now fall down and come out of the shoe. Now's your chance to attack him with your followers.
For wave two it's pretty much the same thing but this time the minions have bottle caps on their heads and you'll need to stomp on them twice. The shoe boss will fall down and pop out, now throw your minions at him.
The third wave the minions have spike helmets which you can't stomp on, so you'll need to use a charge attack by holding the button while your in your big mode. He will now fall down for the last time and pop out, just throw your followers and he will be defeated.