Be aware that if you run the DSO138 from a 9V battery, when the battery gets low, you will start to get incorrect waveform levels. If memory serves, it's to do with the negative voltage reference circuitry not working properly below about 7.5V.
And regardless of method of power supply, you cannot give it less than 7V anyway because it uses a 7805 regulator for the 5V rail which has a 2V dropout voltage.