From the Super Mario Wiki
Tubba's Heart is, as the name implies, the heart of Tubba Blubba removed by Bowser and hidden in the Windy Mill. After having his heart removed Tubba Blubba became invincible, the heart controlling the body as if he is a puppet. However, Mario discovers the heart, and the two battle. It is the first half of Chapter 3's boss in Paper Mario.
Tubba's Heart only has two attacks: one in which it dashes into Mario, and another in which it swarms Mario with heart tissue to deduct 12 HP if not avoided, though the latter requires a turn to charge up, giving Bow the opportunity to use Outta Sight on Mario.
When the heart's HP reaches 5 or lower, it runs away from Mario and escapes the undergrounds of Windy Mill. When it reaches the surface, it sees Tubba Blubba outside and reunites with him. Tubba Blubba eats his heart and becomes vulnerable with his heart inside his body.
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