Tubba Blubba became invincible when his heart was removed by Bowser. Hiding the heart in the Windy Mill, it controlled Tubba like he was a puppet. However, Mario discovered the hairy heart, and the two battled. It is one half of Chapter 3's boss.
Tubba's Heart is one of many examples of characters who bear resemblence in art style to those from Yoshi's Island and Yoshi's Story. Sluggy the Unshaven had a visible, hairy heart as well.