There are several synonyms for the phrase "pounding away." One of the most common is "hammering," which implies a forceful repeated action, similar to the striking of a hammer. Another option is "thumping," which suggests a heavy, rhythmic sound or motion. "Battering" is another possibility, indicating a relentless, forceful attack or effort. "Pummeling" can also be used to convey a sense of intense and repeated physical impact. Additionally, "drumming" is a suitable synonym that describes a steady and repetitive sound or motion, similar to the beat of a drum.