Isn't it right to say "the guard dog OF the Underworld"?
Actually, both "of" and "to" can be used here. When the speaker says "the guard dog to the Underworld," he implies that Cerberus guards the entrance to the Underworld, hence why he has used "to" here. However, you can substitute "of" with "to" without changing the meaning of the sentence. Ex: This is the door to the stairway to heaven. Ex: This is the door of the stairway to heaven.
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