Step 1: Remove Cross Pin

Picture of Remove Cross Pin
Use a needle nose pliers to remove the cross pin.

Step 3: Detach The Cable Housing

Picture of Detach The Cable Housing
Pull the cable housing to the side to free it from the main part of the assembly.

Step 4: Pull The Cable

Picture of Pull The Cable
Grasp the body of the assembly with one hand and the cable housing with the other. Pull the cable out of its housing.

Step 5: Remove The Cable End From The Traveler

Use a pick or a hook to pull the threaded plastic traveler (I am not sure of the manufacturer's name for this piece.) from the body of the assembly through the open upper end (same end covered by the knob before disassembly). Slip the end of the cable out the side of the traveler. To assemble, repeat the steps in reverse. It may be necessary to twist the cable housing on the cable to make it feed properly. Check for excessive wear on the threaded portion of the plastic traveler and the screw shaft. Both are made of softer materials and are likely to show excessive wear. See the second photo. But, gently lifting the aluminum disc from the top of the knob allows removing a screw with a Philips head. Then the old screw shaft slides out. (See the third photo.) 

I was away from my tools for a couple of months, but have now done an Instructable on rebuilding an Achiever's knob adjustment assembly. See it here.