Many batteries will do the job. Many batteries will provide WAY more then their nominal current.
Are you willing to use LiPo batteries?
This battery, by the numbers, could provide 10A for a bit under 2 minutes.
Add in manufacturer exaggeration and some internal resistance and you might get a minute of 10 amps.
The 35C rating says that is can provide 35 times its nominal .3A rating without excessively diminishing the call capacity.
Here are some smaller ones.