How does supply voltage affect `analogRead()` on AVR-based microcontrollers?
The ADC measures a voltage ratio. The conversion result is the rounded
value of 1024×V/Vref, where V is the voltage at the input and
Vref is the voltage reference.
In the default Arduino configuration, the reference is connected to Vcc.
This will not fit your use case, as the voltage you want to read does
not vary proportionately to Vcc. You could use an external reference.
However, the ATtiny85 has two internal voltage references at 1.1 and
2.56 V. Either of these may be well suited for you application,
which should save you having to add an extra part.
See the chapter on the ADC in the datasheet for details on
how to select the voltage reference.