Q: How much would this cost to repair? 2001 Chevrolet Impala

Hi - first task would be to check the transmission fluid level. Also, is the fluid red, or closer to black? If dark in color, it may be a good idea for change the transmission fluid and filter. Check also for problem codes, whether the Check Engine light is on or not. Many auto parts stores will do this for you for free. Given your mileage, there are many possible transmission problems which could occur: low hydraulic pressure in the transmission (worn out pump), sticking or leaking solenoids or valves, or worn out clutch packs. I would recommend a transmission inspection by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, give you an accurate assessment of damage and cost estimate for repairs.