2004 Hyundai Elantra GT P0720 code.
 

So far I've replaced the Output sensor which did not get rid of the codes, have made sure the wires are good, and have done a transmission flush. None of the options have worked and the car still hard shifts, and mutippe times. I can't think of any other reason to solve this.

Did you ever get this resolved? I am currently having the same problem??
The scan till resets it but it just appear after awhile, only way ive driven it so far. After reset and cooling it runs just fine then once it warms up same prob, and I also replaced parts and checked wires on the line.

Possible causes
Input sensor, Output sensor, Transmission fluid temperature sensor, wires, change transmission fluid, fix leaks

I replaced both Input/Output Sensors, checked the trans fluid its red , no leaks and still nothing.. I was leaning at it's more of a computing problem than mechanical. Since at certain part in function its "MIL" goes from OFF to ON and then it detects the problem. Something is being switched to a different setting. Any advice/hints/prior experience at which electrical component could it be?

Replacing good parts can get expensive and still not correct the problem.
Good move to have a qualified shop check the entire vehicle for the problem.
Not all similar symptoms are caused by the same thing.