In the rulebook, under Resolving an Engagement - Step 5 Pg. 20 -
A player does not have the option to pass during thisstep. If he has at least one ready participating unit, it must focus to strike.
and pg. 23 concluding the resolve strikes step - After all units participating in the engagement are exhausted (either by striking, by receiving a focus token during a ∫ icon resolution, or by other card effects), the resolve strikes step is over.
The unopposed extra damage is awarded in Step 6 after the above has been completed.
Would this mean that if Red 2 goes in unopposed and destroys the objective using the Unopposed bonus, he would be ready coming out of the battle?
I think it would as the damage was dealt after the Resolve Strike step which requires all participants to be focused. Step 6 has no such requirement.