If you are referring to her character (rather than her skills), option 1 is natural and common, but option 2 sounds unnatural and awkward. If you are refer to skills, it would be natural to say “She is not that good” (omitting the word “person”). Example: “Do you think she can qualify for the Olympics?” “No way, she’s good, but she’s not that good.”

You could say: He is not that good of a person if he did something that dishonest. Another example could be: She is not that good of a pianist after hearing her performance.

1) ''He is not that good a person!'' A better option is "He is not that good of a person!" Like your example, this is used in response to someone's suggestion that the "he" in question might do something good. You disagree and declare that "he" is not that good of a person. 2) ''She is not a person that good!'' This construction is awkward, and while a native English speaker may understand what you are trying to say, it will require some effort on their part as it is not the construction normally used to express the idea you are trying to convey.