Gear shifter difficult to shift?

Yes, worn out shifter cable will cause this problem. Here is how to change them out and make any adjustments needed. Check out the images (below). Please upload pictures or videos in your response to any problems so we can see what to help you with.

I thought I can make the adjustment without removing it from the transmission in the engine bay. From previous cobalt owners, they placed shifter in Neutral and then made markings with permanent pen marker and then lifted the plastic holders making sure shifter is still in Neutral and then the placed the plastic holder back on?

Correct, you don't have to remove the transmission from the engine bay.

So, I made sure the gear shift was in the center for Neutral. I then lifted the plastic lids off each cable, and I immediately saw the second cable move from where it was. I then placed the plastic lids on the cables locking them in place. Test drove the vehicle. Was able to shift into third gear but the fourth still getting grinding and not going into fourth as easy. I know it's a fifth gear so while trying to get it in fourth not to accidentally put it in reverse since it's near that gear.

I didn’t push the Neutral Lock clip inwards. I made sure it was in its Neutral position when I lifted the lock tabs. The Neutral Lock is in the same position and I also didn’t disconnect the cables from the transmission.

Yep, it sounds like the cables has gone bad and has allowed the shift cable adjustment to become off, I would replace the cables by following the instructions above. Chances are the adjustment will change again with the old cables.