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My dream is to make it as a Hollywood actor.
Literal
I [of-の] dream [topic-は] Hollywood [of-の] actor [as-として] succeed thing is.
Topic-comment structure defining a dream. として marks 'as, in the capacity of' — 'succeed AS an actor.' The 事 at the end nominalizes the preceding clause so it can be the complement of だ/です. A standard introduction for aspirational statements.