Step 1: Analyzing bond order.
Bond order is defined as the number of bonding electrons minus the number of antibonding electrons, divided by two. The species with the highest bond order will have the most stable bonding.
Step 2: Conclusion.
The correct trend in bond order is O$^{2+}$>O$_2^{2-}$>O$_2$. The bond order increases as the number of bonding electrons increases.