Step 1: Conceptual Understanding:
Bond order determines bond strength.
Step 2: Explanation in Detail:
Bond order: $\mathrm{O_2}$ (2), $\mathrm{O_2^-}$ (1.5), $\mathrm{O_2^{2-}}$ (1). Bond strength decreases with bond order.
Step 3: Therefore, Stating the Final Answer
$\mathrm{O}_2>\mathrm{O}_2^->\mathrm{O}_2^{2-}$.