Pi Zero battery backpack case using a Samsung S5 Li-ion.

thingiverse

I think this offers one of the highest compactness to battery capacity ratios for a pi Zero, which is very ideal for a number of projects. You can get HATS for AAs or other LiPos, but nothing beats a good old widely available smartphone battery. Especially since it takes up little space around the Pi. A 100mAH battery lasts about 20min running the pi Zero, so 2500mAH should last about 7.5 hours constant draw. Samsung S5 Batteries are very reliable and pack 2500-3000mAH of charge. You can find many aftermarket ones, the OEM is $11 CDN on Amazon. Because it's 3.8V you're going to need some sort of 5V voltage regulator. I would suggest an Adafruit 1000C. They're pretty small so it wouldn't be any more significant space. Mounting one to one of the Pi's corners and directly to the GPIOs would be the best bet, I think. The print in the pictures was my first version without the ledge, so I melted a ledge before updating to the current CAD model. The heat gun melted a little too much on it but oh well the new one works perfect, no melting required lol.