If Xiang Yu Had Cultivated Immortality, How Could He Have Died at the Wu River?

A young man from the twenty-first century transmigrates two thousand years into the past and takes over the body of Xiang Ji, the great Conqueror. He brings along a Bone-Illuminating Mirror. I have a Bone-Illuminating Mirror that can reveal my true self, and it even comes with secret cultivation techniques.