The phrase "hadst at it" refers to someone actively engaging in a task or activity. There are several synonyms that can be used to convey the same meaning as "hadst at it." For example, some may say "going at it," "working on it," or "tackling the task." Other phrases that are similar include "putting in the effort," "doubling down," or "determinedly pursuing the goal." No matter which synonym is chosen, they all signify an individual putting in hard work and effort to successfully complete a task or activity.