The phrase, "having at" can be a little tricky to find synonyms for as it has a specific connotation. However, some potential alternatives could be: attacking, going after, pursuing, confronting, engaging, or grappling with. Depending on the context, there are other possibilities such as battling, contending, resisting, tackling, or challenging. It's important to keep in mind the specific meaning that "having at" carries and choose a synonym that accurately reflects that meaning for the situation. By understanding the nuances of language and word choices, you can communicate more effectively and clearly.