I have a lightly used Diamondback Axis XE that I've been having a minor front derailleur shifting problem. It is difficult to search for, I've read a few derailleur threads but nothing with these same symptoms.

Downshifting (going to big-little cog, this is a triple chainring) is fine, however upshifting (small to big) take pushing the shifter to its stop and holding it there until the shift completes. No chain rub or derailleur misalignment. Front derailleur is a Shimano TX50. Would this be a cable issue, or do I need to adjust the derailleur itself?

Increase the tension in the cable. There is usually a barrel adjuster on the shifter itself or on one of the braze ons on the downtube. Alternatively just shift to the smallest chainring and pull the cable a little tighter.

Great, I will try that. I was hoping it was something relatively simple, not too comfortable with adjusting the derailleur yet.

Remember, to INCREASE the cable tension you're actually UNSCREWING the barrel adjusters. (Counterclockwise.) It'll be easiest to do this in the smallest chainring.

Follow this procedure from the beginning as if you were doing a new installation: Front Derailleur Adjustment - Park Tool
You need to do the steps in order since the later steps depend upon the previous ones being done correctly. Tweaking one adjustment when you do not know if the others are correct may not go as well as hoped.

How is your Technique? take off all driving tension from the chain when you want it to climb up to a much larger chainring,

dont Force It.

give it, the Shift , the Slack .. Spin without pedal pressure..

I've looked through that guide, certainly made it seem like adjustment wasn't that big of a deal.

This is one of the things I thought of when I noticed it wasn't shifting as it should. I want to say I slacked off the pedal pressure when shifting, but I'm not sure. I'll try it again without pressure and see what it does to make sure I'm not the problem.

If it shifts OK while on the repair stand, it may be you are not letting it work as well as it Can.