Sentence contains the participle phrase <em>walking on the beach.</em> A participle phrase will begin with a present or past participle. In this case, it begins with a present participle <em>walking.</em> As all phrases require two or more words, a participle phrase might include objects and/or modifiers that complete the thought (the PP <em>on the beach). </em>
Moreover, participle phrases always function as adjectives, adding description to the sentence. In the sentence above, the participle phrase modifies the noun <em>Delores. </em>