Which of the following species is diamagnetic?

The correct option is D $O_2^{2-}$
In the given species, all electrons are paired in orbitals except in ${\pi }_{\left(2p_x\right)}^{\ast }$ and ${\pi }_{\left(2p_y\right)}^{\ast }$.
The presence or absence of unpaired electrons in these two orbitals determine the magnetic behavior.
The number of unpaired electrons in various species are listed below.
$O_2^{+}:{\pi }_{(2p_x{)}^1,}^{\ast }{\pi }_{(2p_y{)}^0}^{\ast }$ contains one unpaired electron.
Hence, it is paramagnetic.
$O_2:{\pi }_{(2p_x{)}^1,}^{\ast }{\pi }_{(2p_y{)}^1}^{\ast }$ contains two unpaired electrons.
Hence, it is paramagnetic.
$O_2^{-}:{\pi }_{(2p_x{)}^2,}^{\ast }{\pi }_{(2p_y{)}^1}^{\ast }$ contains one unpaired electron.
Hence, it is paramagnetic.
$O_2^{2-}:{\pi }_{(2p_x{)}^2,}^{\ast },{\pi }_{(2p_y{)}^2}^{\ast }$ contains no unpaired electron.
Hence, it is diamagnetic.