When one is "insistent on" something, they are strongly determined to make it happen or obtain it. There are several synonyms for this phrase, including persistent, resolute, unwavering, determined, unyielding, and steadfast. These words all carry a sense of determination and commitment, indicating that the person in question will not easily be deterred from their goal. Using synonyms for "insistent on" can help to add variety to your writing and better convey the meaning behind the phrase. When choosing a synonym, be sure to consider the context and tone of your writing to ensure that your language accurately reflects your intended message.