Final answer:
The sentence uses the rhetorical device of parallel structure, which creates a repetitive and emphatic rhythm that highlights the determination of the speaker.
Step-by-step explanation:
The rhetorical device used in the sentence "I will meet any challenge, overcome any obstacle, and beat any rival that comes my way" is parallel structure. This device involves using the same pattern of words to show that two or more ideas have the same level of importance. In this case, the parallel structure is crafted through the repetition of the structure 'I will [verb phrase], which organizes the sentence rhythmically and emphatically, emphasizing the determination of the speaker. The use of this device underscores the writer's intent to consciously meet or challenge conventional expectations in rhetorically effective ways. While there is a sense of repetition in the structure, it's primarily the parallelism that stands out in creating a powerful oratorical effect.