It's "Supercapacitor", an electrochemical device that acts like a massive capacitor - Five FARADS for the one in the link;
ie. five million microfarads.
Two or three of those, in parallel with a 4.2V battery pack, would boost the peak current to the type of range you need.
Basic electrical definition:
One farad with 1A current (= one coulomb of charge per second) will change voltage (charging or discharging) at 1V per second.
With 5F and 5A load per device(shared over as many as needed), if the motors start in 1/10th of a second, the voltage would only drop 100mV during startup & the battery would top up the supercap while the motor idled.