This achievement requires that you have one Sim become nemeses with 16 other Sims simultaneously. In order to obtain this achievement, you must have at least 17 Sims in your town. This will not be possible until you reach Level 22. Once you have 17 Sims, choose one to be hated by everyone. Use the "Complain" (requires 30 interactions and 5 total minutes) or "Be Rude" (requires 10 interactions and 10 total minutes) interactions over and over with another Sim until you drop to the Nemesis relationship. Continue the process until one Sim is nemeses with 16 others. Note that you cannot negatively interact with babies or toddlers (so age them), or anyone that your a best friends with. Preteens are fair game though.