I don't know the exact numbers (and they depend at least partially on how often you're using Tessel's wifi), but I would guess Tessel 2 is drawing ~300mA average, with around 500mA peak. So you'll need a battery that can supply 300 mA* (1/2 hour) = 150mAh with a max current of 500mA or more and a rated voltage of 3.3V-5V. You may want to add some buffer mAh in case my estimates weren't conservative enough. Usually, T2 is powered by 5V so its USB ports can also be powered at the standard 5V and I honestly don't know what happens if they have less than that supplied. I think the rest of the board should be fine.
One reasonable choice would be this 400mAh battery from Sparkfun.
Keep in mind that to connect it to Tessel, you'll need to also buy the JST mating connector and solder it into the GND and 5VIN pins on the Tessel.