When you do something single-handedly, you do it on your own, with no help from anyone else. Superheroes are known for single-handedly defeating bad guys.
Use the adverb single-handedly when a person achieves something independently, especially when it's especially admirable or difficult. Your mom might have single-handedly raised you and your siblings, or you might try to single-handedly move a dining room table out the front door before your yard sale. Single-handedly comes from the adjective single-handed, or "done without help," and both words have been in use since the early 1700's.