There are various synonyms for the phrase "achieve an aim," which refers to accomplishing a particular goal. One synonym for this phrase is "attain a target," which means hitting a specific objective. Another synonym is "realize an ambition," which refers to achieving a long-standing desired outcome. "Fulfill a purpose" is another synonym, which means bringing a plan or objective to completion. "Accomplish a mission" and "complete a project" are also synonyms that can be used to describe achieving a particular aim. Ultimately, there are many synonymous phrases that can be used to express the idea of successfully achieving a goal or objective.