There are a number of synonyms you can use for the phrase "with bad intent" depending on the context of the sentence. Some of the most common alternatives include "maliciously," "malevolently," "vindictively," "spitefully," "harmfully," and "detrimentally." Other options might also include "nastily," "venomously," "viciously," "cruelly," and "hurtfully." Ultimately, the word you choose will depend on the tone and meaning you are trying to convey, so it's important to consider your options carefully and choose the one that best captures the idea you are trying to express.