Yes, it is possible to replace the battery, but it is anything but a simple procedure, and there's a decent chance you'll end up killing the Garmin in the process. It was not designed to be user-serviceable, at all.
As I recommended above, just get a small external USB battery pack and plug the Garmin into it at the start of your ride. The 820's internal battery is like 700mAh-- a $10 "lipstick" USB pack will be 3,000mAh.
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