How do i upgrade my general under honourable conditions discharge to an honourable discharge? Will I have a better chance of reenlistment?

Depending on when you left service, you can go through the VA or if it’s been a long enough amount of time you can apply to the board of corrections to military records

Like the comments, you need to get character references to present to the board, the va does not change your discharge. The VA can for their purposes change rour right to get VA care.

How?

Not knowing more details than what you've given I can only point to a buddy of mine that was booted out and after a few years was able to have his dishonorable changed to honorable. In HIS case it was DADT and it always bothered him that he had a dishonorable discharge so he fought it. It took him almost a decade but he was able to get it changed. I doubt yours will be that bad but your still going to have to fight. Talk to the local chapter of the VA in your area and ask for help.

What is your goal? Is it to qualify for VA benefits or is it returning to military service? I can address returning to service because I personally fell into this category, re-enlisted, and eventually retired from the Air Force as a Master sergeant.. First determine whether your re-enlistment codes allow you to re-enlist. Either search on Google or take your DD-214 to a recruiter and ask. You many have to try several recruiters before you find one willing to do the work, but it can be done. My recommendation is to try the Army National Guard first. Every unit has one or more recruiters dedicated to that unit. Find a unit that is well below !00% strength because their recruiter will be more willing to work with you than one that is at or above 100% strength. Good luck!

it can be done with a waiver if you have an RE3 a 4 you are not eligible to enlist. Normally it takes 6 months depending on what u were discharged for

https://www.va.gov/discharge-upgrade-instructions/

Good lick

Go to your local Federal Building, and ask to see the Veterans Rep.

What ever you do, you will have start by obtaining and filling out a DD 293.

While I was recruiting this question showed up more often than not. The board that makes those decisions has a 80% or so "No". Unless you have a good reason and multiple letters of recommendation from ranking individuals, you are SOL.