Modify PCB Mains Voltage input to 12VDC
First thing would be to confirm the output voltages of whatever the existing power supply. If it only outputs a single 12V supply, then you can connect a 12V battery to the output of the power supply section. But remember, typical lead acid batteries can be charged up to 14.4V and your amplifier should be able to withstand that. Also, it would be better if you connect the negative wire to the PCB instead of the heat sink.
Anyway, more information can be given if you provide a schematic or a model number of you amplifier.