The character of the half-man, half-beast servant of Prospero, Caliban, embodies all the characteristics of a tragic hero. At first it is quite difficult to see whatever heroic attributes could be given to him, but when you analyze his main problem, and the obstacles to solve it, he almost become as pitied by the audience as well as feared.
First, Caliban is grotesque, monstrous and scary. In a horribly ironic contrast, he always speaks in verse form, and the language he chooses to convey the message of the love for his island are full of figurative language, and completely convey emotion.
Second, he shares both the characteristics of man and animal. One part of him is hungry for taking back his beloved island while another part of him wants to rape Miranda, and kill Prospero. This duality in character definitely creates tragedy in his life.
Finally, when it comes down to reality, the land that Caliban loved so much was, indeed, ursurped by Prospero. It is Caliban who first lives there and shows everbody around with tremendous pride. His anger is not unjustified. It is the way that he utilizes his anger, and the conflict of his dual personality, what makes it almost impossible for him to change his current reality.
Therefore, Caliban is certainly a tragic hero in Shakespeare's The Tempest.
Caliban is a tragic character because Propspero is cruel to him and punishes him, although Caliban did attempt rape on his daughter Miranda so it is understandable.