if someone or something is defending or fighting with the heart of a warrior, this means that they have the same passion as a warrior does as he goes into battle. "passion" is one of your choices, so i'd definitely mark that one, because the guard dog is using the same ferocity and passion that a warrior would. "heart" in this case also refers to "courage" and "spirit." one way to answer this question is to try and swap out the word "heart" for any of the answer choices, and see which ones help the sentence keep the same meaning.
a dog fighting with the passion of a warrior still gives you the same vibe as a dog fighting with the heart of a warrior. a dog fighting with the courage of a warrior also gives you the same impression, a guard dog with the spirit of a warrior as well.
