What are the odds of converting a TAPMI call for a fresher (BBA) with 88% in CAT, 10th - 78, 12th - 79 and grad 66?

Even though your 10th and 12th-grade graduation rates are low, you have a good chance. I think you will convert it if you do well on the GD/PI. A lot depends on your resume, including your extracurricular activities and other things. As the final selection is based on multiple factors and a person with a good profile has a high chance of getting into TAPMI.

TAPMI uses Profile-based Shortlisting. Shortlisted profiles include:

• Valid CAT/XAT/GMAT/NMAT/CMAT scores (higher)
• Academic Performance (10th, 12th, Graduation, Overall)
• Work Experience (Company, Months)
• Extracurricular Achievements (State/National/International if any)
• SOP: Statement Of Purpose

Below is a list of courses offered and CAT percentile required to qualify: