Mightily rhymes with:
vitally, accidentally, anecdotally, atalie, brutally, coincidentally, continentally, digitally, environmentally, experimentally, fatally, fundamentally, governmentally, hastily, heartily, horizontally, incidentally, incrementally, italy, jauntily, mentally, monumentally, mortally, natalie, nathalie, nattily, ornamentally, ottilie, philately, scantily, subtly, temperamentally, testily, totally, vitally, wittily
Mightily sounds like:
macdill, macdowell, machtley, macktal, magdala, mastel, mcdeal, mcdill, mcdole, mcdowall, mcdowell, megadeal, migdal, minoxidil, mostly