Adjusting rear derailleur - shifts to lower gear, but not to higher
Perhaps your shifter cable can't slide smoothly. Shift to the tallest gear (smallest cog). Pop the shifter housing out of the brazed-on stops. Slide the housing back and forth and look for stiffness. Put some lube in the housing and slide it back and forth to distribute it. 

Perhaps your derailleur hanger is bent. A bike shop will have a tool to easily check its alignment.

If either of these is a factor, then you will never be able to adjust your shifting properly.