Okay, something weird just happened. I decided to beat Dark Inferno in the main game to see if that would cause my next victory over Data Dark Riku to raise my progress towards Analysis Complete. After defeating Dark Inferno, I saved, returned to the title screen, and went back into Limitcut. I checked my progress before I went in to fight Data Dark Riku and it had gone up from 23% to 30%. Thinking back, I don't think I checked my progress between my victories against Data Young Xehanort and Data Larxene the day my progress finally increased from 15% to 23%. Perhaps Data Young Xehanort alone was responsible for raising my progress that time. I think the solution is "If your progress doesn't increase after a legitimate victory, beat a different boss to get the victory to register in the achievement bar." I'll try that next time my progress doesn't go up.