What is the true shape of Earth's orbit?
The Earth's orbit is approximately elliptical but constantly changing.
Actually the Earth doesn't orbit around the Sun. A barycentre is the centre of mass of two or more bodies. The Earth-Moon barycentre orbits around the solar system barycentre. The Earth and the Moon both orbit around the Earth Moon barycentre. The Sun also orbits around the solar system barycentre which is actually above the surface of the Sun.
The Earth's orbit is approximately an ellipse. The shape and orientation of the orbit are constantly being altered by the gravitational pull of the Moon and the other planets. To emphasise this the Earth is at perihelion around the 3rd January. Perihelion 2016 was on 2 January, perihelion 2017 will be on 4 January. This variation in perihelion is due to the gravitational pull of the Sun, Moon and other planets.
So, the Earth's orbit does not have an exact shape. It is constantly changing.