Here’s a design guidelines for ATtiny43U from Atmel, app note here (PDF!):
The integrated boost converter of ATtiny43U provides the microcontroller and peripherals with a fixed supply voltage, generated from an external supply of lower voltage. The boost converter is a switching type, step-up regulator that requires
some external components to be complete. This includes an external inductor, a diode and some bypass capacitors. The inductor is connected between the VBAT node and the LSW pin, and the Schottky diode between pins LSW and VCC. In addition, an input capacitor and external bypass capacitor from VCC to GND areusually required.
The good: Boost regulator starts from as low as 0.7V.
The bad: Load capability never explicitly discussed, but charts go up to 30mA only. A regulated-overloaded chart in the MCU DS has a slope of around 30ohm, so its NMOS switch is like a high-load MCU I/O pin, for comparison MCP1640’s NMOS switch is ~0.6ohm. The inductor is a bit surprising too, they specified 15uH when most ~100kHz switchers use values in the 47uH range… hmmm, any idea why? (Low load capability, no need so much energy storage?)
Obviously enough for cost-sensitive stuff with segmented LCD and beeping, but for prototyping, users might fall into the trap of not-enough-amperes like RPis with weak power-supplies.