It's 10M of bullet LEDs, a Pi Zero W and a USB powerbank. The lights are just safety pinned in at the moment whilst I fiddle with things to get it right. I was going to go with strips but figured that bullets would be less likely to get damaged with twisting/flexing. I haven't performed a full battery test but it seems to get about 1-2 hours with the lights on and around 6-7 hours 'standby' (with just the Pi Zero wifi turned on).
Currently trying to think of a way to get a cable from the Pi up to a hat cleanly. I need to figure out a way that's unobtrusive and easy to take on/off.