Powering ATtiny85 with 4 AA batteries

jremington:
Nothing in the above statement is correct.

Diodes have an exponential current/voltage relationship.

The uP does not expect constant voltage, and as stated, can run from about 1.8 - 5.5 V.

The diode has fairly linear relationship from 0 to about 0.3V. Only > 0.4+ it behaves exponentially.
If the uP or its regulator is fine with whatever however voltage it is being fed then I don't know the point of using more capacitor that is supposedly keeps the diode from imparing the uP operation.