You don't have to remove the axle and differential. Just jack up the ATV under the engine and remove the pivot bolts on each side of the frame that holds the swing arm on. Then, remove the whole swing arm, differential, and axle as an assembly. You can change the rubber u-joint boot while you have the swing arm off, since the drive shaft will come out with the swing arm.
If you don't have the service manual, go to the link below and download it and it will show you how to remove the swing arm. Look in the "Rear Wheel/Suspension" section under "Swing Arm". Just ignore the part about removing the axle and diff and just remove the brake cables, shock, and the swing arm pivot bolts.
Service Manual Downloads - All years