The small end of the pinion shaft rides in a needle bearing, but all the needle bearings are probably gone......they usually are. And that just leaves the bearing race that has to be removed from the case. The old needle bearing race is a PITA to get out. You have to remove the keeper ring through the tiny hole in the side of the diff case where the needle bearing sits before you can knock the needle bearing out. Even after you get the keeper ring out, it's still hard to get the old needle bearing out. To get the top pinion bearing out, you have to have a special tool to remove the lock nut. But you can make the tool by welding a deep well impact socket to a large nut of the correct side to fit down inside the lock nut. Once you get the two pinion bearings replaced, it's easy to knock the two diff side bearings and seals out and put the new bearings and seals back in.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.