A guy is climbing around on the statue of liberty back in the 80's during the refurbishment some construction guys are trying to kill him but he beats them then is chased by another guy who falls in wet cement

Yes, the movie is Remo Williams: Remo Williams: The Adventure Begins (1985) - IMDb (http://www.imdb.com/title/tt0089901/?ref_=nv_sr_2)