Answer
$O^{3-}$ does not exist because it would not be stable.
Work Step by Step
When $O^{2-}$ is created all the orbitals in shell 2 are filled. If another electron is added it would have to exist in a new shell layer. Shell 3 is further from the nucleus and is shielded from the nuclear charge by the electrons in Shells 1 and 2. The weaker nuclear attraction for this 11th electron is not strong enough to overcome the electron repulsion, so a stable $O^{3-}$ particle cannot be formed.
