How did the battle of waterloo contribute to Napoleons downfall

It was the final struggle over who would win in the war of napoleon, napoleon and his army fought the armies of the coalition at the battle and napoleon would have won, but at the last second another army from some other nation (s) came at the last second and the coalition was victorious. Kind of like lord of the rings when helms deep was under siege by isengaurd and at the last second Gandalf came with riders of Rohan