I often think about this while writing or trying to articulate whether or not something is objectively of a high quality or is subjectively catered to my interests.
The first stop on finding out comes from looking at the definitions of the words, as you should always always always do. A character is defined as a person in a story. That's about it. Good in the qualitative sense is defined as the standard of something as measured against other things of a similar kind; the degree of excellence of something.
So, saying a character is a good character in a technical sense is completely subjective. What you personally set as a standard is what dictates what you find to be a good character. What you personally value is what has value.
From the general sense, I'd say a character that is consistent is the closest thing to being objectively good. A character that is established to have a pattern of thought and that the writer sticks to it.
One way to tell is to try and write a fanfic of something. This is why fanfiction is actually a great writing exercise, because you're taking pre-existing characters and putting them into your own scenarios. If the character has enough personality and thought put into their creation, anyone should be able to write that character into other, completely original situations and have them act and react as though it was the original writer putting them in there.
This is why Mary Sue characters are so often looked down on, they're only there to serve whatever purpose the writer wants and are given very little personality to accompany it. Kirito has very little personality, so he can be written into just about any scenario and have it work.
A good character has a personality and a mind of its own. You'll often hear writers refer to their characters as their children. That's because that's what it feels like. You're giving an idea an identity of its own, a good character should be a breathing and living thing. Not a plot device.
At least to me, that's a good character.