Charged extra high by an automobile repair shop

My car's battery had a loose connection. My car was hence towed to S&I repair shop in Metairie by AAA.I told the S&I people that my car battery is entirely new. The reason my car did not start is either due to loose cable connections in the battery or overheating of car because of less coolant.

The car was kept for 2-3 hours but the work was done on the car only for few minutes. And what they did is just tighten the cables. Now the technician told me that car also needs Tune-up and it will require $279 for tune-up. I told them that tune-up charges are overly high and just charge me for whatever work you have done. They then charged me $75($69+Tax) just for tightening the cable and told me that $37 will be taken-off if I did the tune-up (a sort of blackmail). I paid the $75 and left the place.