2003 cavalier trac off/ jumpy tach/ hard shift

You’re describing a transmission that is slipping. And if the transmission starts to slip it will go into what is called the limp mode. When in the limp mode, the TRAC light will come on because the transmission is malfunctioning. If the transmission is slipping the tach will be erratic especially between shifts. And finally, when the transmission goes into the limp mode, the ECU will raise the line pressures within the transmission to prevent further damage. And this is what causes the rough/hard shifts.

Have you checked the level/condition of the transmission fluid?

Tester