How Do I Fix This Annoying Transmission Slipping Issue?

I've got a '97 Nissan Altima with 170k miles and I'm experiencing a transmission slipping issue. It happens when I accelerate from a stop or when shifting into higher gears. The problem seems to be getting worse over time. I've checked the fluid level and it's at the recommended level, but I'm not sure what else could be causing this. Has anyone else dealt with this issue on their Altima? What repairs did you have to make?