what causes my 2001 SW2 (135k miles) Automatic Transmission was shifting hard into all gears and reverse.

What are the code/s?

Fault code is P0133

Just to add to this one i have never seen a bad engine mount cause trouble codes to set in the computer.The P0133 is a bad front o2 sensor the one screwed into the exhaust manifold.I have replaced tons of them for that code.Now for the hard shifts that probably caused by too much line pressure in the transmission.Thats pretty common on that car you will have to do a transmission pressure test to make sure.I need the pressures with the car fully warmed up.I need the pressures in park neutral and drive.Also idling in park with the trs LP fuse pulled.Also make sure the trs LP fuse isnt blown.

Did all checks listed in your response all check normal. However he did not check the idling pressure with the trs LP fuse pulled he states that on this car that makes no difference. All fused are OK. He is now wanting to look into the issue being internal to the transmission. What do you recommend from here?

When you pull the trs LP fuse in park the line pressure will read full line pressure.So yes that test and pressure is important it lets you know how the line pressure actuator is responding and also how the pressure regulator is working.I wouldnt be going inside the transmisionfor hard shifting into every gear and banging into reverse.That is caused by a excessive pressure issue.Those cars are well known for bad pressure regulators being stuck worn bores in the valve for the pressure regulator.Also the pressure regulator springs break causing issues.Could you please get me the actual pressure readings from the ones i asked for including the one in park with the trs LP fuse pulled.There is also a step pressure test you can do but it takes a tech2 scan tool what it does is command the pressures from low to high and they have to be within 10psi of commanded pressure.That is a test you use to find a hard to find problem or intermintant problem.Most of the time you can find the problem with the other pressure readings i mentioned.Also has he driven it with a pressure tester watching the pressures while it shifts hard?Just so you can feel at ease listening to me i worked for saturn for over 16yrs iam a factory trained saturn tech.