Powering AC Guitar effects processor with a batteries
The operating manual for the product says it requires a 9V 3A power supply. In practice the device can probably handle a reasonable input voltage range around this value, but you should probably not mess around with this too much. This means you will probably need to use some sort of voltage regulator to ensure that a constant 9V is supplied to the unit as the battery voltage discharges.

For best efficiency you should get a small dc-dc converter and use this to regulate the output of a 12V battery. You can use any battery you want provided it can supply the current required and has the capacity you need.