Mightily denotes strength and power, and synonyms for it include forcefully, vigorously, strongly, powerfully, energetically, robustly, vigorously, sturdily, significantly, potently, dynamically, intensively, heartily, and emphatically. Depending on the context, one of these synonyms can be used to replace mightily. For instance, instead of saying "he fought mightily," one can say "he fought forcefully" or "he fought with great vigor." Similarly, "she sang mightily" could be replaced with "she sang powerfully" or "she sang with great energy." In summary, there are several synonyms for mightily, and their usage depends on the context of the sentence.