How to replace main bearings on 2.2 chevy cavalier 2000 without having to pull the engine out

You can't. To replace the main bearings you need to remove the crankshaft. To remove the crankshaft you must remove the flywheel. To remove the flywheel, you must remove the transmission. The transmission is part of the engine mounting system. Just buck up and pull the whole works. Chances are you will need to re-bore the mains anyway if you have spun any of the main bearings. That cannot be done with the engine in the car.