How to repair buckled duct work inside wall?
As has been well stated in the comments thread above, your solution may stem more from tuning the HVAC system and your home than repairing this minor obstruction. Chances are you won't see much benefit from a time-consuming repair. 

The suggestions given are good: 


Examine the overall airflow paths for the space. Close heat supplies and returns to force more heat to the cooler areas and draw more air from them. 
Consider the passive effect of open doorways, etc., and make adjustments to how you use them. 
Consider a duct booster fan to pull more return air through the existing upstairs return. This can probably be installed in an accessible location near the furnace. 


Any home needs seasonal tuning. You may need to reverse these changes for the heating and cooling seasons.