We all agree that the actual Robin is a coward, and that the song is false. But what about the Robin of the song. According to the popular definition of courage, one is courageous if one either lacks fear or ignores danger, and certainly the Robin of the song satisfies that requirement. However, Aristotle's definition of courage suggests that a courageous person lacks (or fails to act upon) fear, or ignores danger, to the extent that it is rational to do so. This courage in facing danger can be defective, in which case the person is cowardly, on the mean, in which case the person is courageous, or excessively, in which case the person is foolhardy, and hence does not possess the virtue of courage.
Notice also that it is possible for someone to "bravely run away," if we accept Aristotle's account of courage, however paradoxical that may seem. The reason Sir Robin is a coward is because the three-headed monster is bickering with itself, and hence cannot possibly be as dangerous as it might appear to be at first. Robin doesn't think long enough to figure that out, instead he "turned his tail and fled."