There are several synonyms for the phrase "beat up against." Some common options include "pound against," "crash into," "buffet," and "strike." Each of these alternatives conveys the idea of forceful impact, as when waves beat up against the shore or wind gusts buffet against a building. Other possible synonyms might include "ram," "slam," "pelt," and "assail," all of which evoke a sense of aggressive, even violent, action. Using varied synonyms can help writers avoid repetition and capture different nuances of meaning, adding depth and interest to their language.