Once you have a replacement battery, it should be fairly straightforward. By inserting something suitably narrow a millimetre or so into the gap (watch out for the two flex cables near the centre though) between the rear and the bottom of the Cosmo and prying gently, the back cover should pop off (almost too) easily. On the Gemini, it was necessary to remove a (top) cover to insert a SIM and/or SD card, so it came with a thin piece of metal for the purpose. It works well for removing the rear cover from a Cosmo as well, so I guess something similar would be included with a replacement Cosmo battery, but if not, finding a suitable object shouldn't be hard.
Anyway, the battery compartment of a Cosmo looks like this (I hid the serial/IMEI numbers with that piece of paper):
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In the Gemini, the battery is held into place with a bit of adhesive. I'm not sure about that in the Cosmo, but the thin metal plate (which the Gemini doesn't have) may suggest it's just held in by a few screws. On the Gemini, it's necessary to remove a few screws to get to the battery connector, and it seems to be the same with the Cosmo.
Overall, while the Cosmo (and Gemini) battery isn't designed to be swapped out when empty, it is designed to be replaced when worn out. As far as I know, both the Gemini and the Cosmo uses the same size and type of battery. As of now, Gemini owners in need can apparently contact Planet support to purchase a replacement battery, though from what I've read elsewhere in this forum, deliveries seems to currently be very slow, if happening at all. Reasonably that will improve over time, most likely long before any Cosmo owner will need replacements.
