In the book by J.R.R. Tolkien and in the third Hobbit film, Bard kills Smaug by firing his final black arrow into the one spot on Smaug not covered in protective scales.

The Hobbit Film Trilogy Explores Bard More Thoroughly The book does not introduce Bard until Smaug is flying over his home, Lake-town, but the films set up his character earlier.