Best way to communicate Raspberry Pi and ATTiny13
You can use standard I2C or SPI. Master implementations exist for Raspberry Pi, and slave implementations exist for AVR. Using TinyAVR seriously limits usage for a very basic processing, so maybe you should opt for AVR with more memory if that becomes the problem. You can also use RS485 single master multi slaves serial communication over Pi's RS232 if RS485 interface chips are used on Pi and all AVRs. Of course, in this case you must implement some known standard protocol or create your own custom protocol.