Li-po batteries are very good to supply large current. I just tested
"Tenergy 7.4V 900mAh, 25C High Power Lipo Pack"
on Nybble.

It seems that with its super power, the protection in NyBoard's step down chip will always be the bottleneck. So it's a must to bypass it as discussed in previous post.
It's also recommended to design a customized battery mount to replace the original one on the belly, to keep the center of mass low and symmetric.
I use LiPo's for most of my hobby projects and have a nice flat 2S 1000mah for my Nybble. Instead of battery compartments, what works well is just a bit of self-adhesive velcro on Nybble and battery. Easy low cost solution and you can even move battery a bit around if you want to play with center of gravity.
So from some digging I expect these AA size EBL batteries are rated for ~1.0C or about 850mA max discharge in series (based on all the similar form factor datasheets I could find). I'm guessing things work because moves are a bit "bursty" on the current.
I was thinking I'd put of pair of Jauch 1.9Ah 3.7 with a 2C rating (e.g. Digikey 1908-1372-ND). This should then be good for 1.9A steady state (providing significantly more headroom) and essentially the same weight and physical envelope as the battery holder. Maybe instead the pack 1568-1876-ND, but it may be too wide and long. I'm only now starting to assemble so I don't have a good since of the true maximum.
@Rongzhong Li What are your thoughts on shimming the legs out a few millimeters (and what are the real maximum dimensions?
When connecting batteries in serial, it’s very important to use same batteries to avoid unbalanced loads. To work with Nybble, the maximal discharging rate also matters. The battery should be able to handle >3.5A without shutting down the current. It’s ok the change the terminal plugs as long as the direction is correct.