Build remote wireless Wake-Up with Attiny85
You haven't indicated any minimum distance requirements, so I'd consider using a pair of resonantly coupled inductive coils to wirelessly wake your ATTINY85. 

This solution is particularly compelling because the receiver requires no power at all. 

Here is a very simple circuit that could do the job...







simulate this circuit &ndash; Schematic created using CircuitLab

The transmitter could be as simple as a sine wave generator connected to a coil. 

The AC current in the transmit coil will generate a magnetic field that will induce an AC voltage in the receiving coil. When this voltage rises above the threshold voltage on pin INT0 on the ATTINY then it can trigger that chip to wake from deep sleep. The zeener diode limits the maximum forward voltage that pin INT0 sees.

The distance between the transmitter and receiver will be dependent on the size of the coils, the number of turns they have, their geometric configuration (co-axial best), and the driving current and frequency on the transmit coil. You can google "resonant wireless power" for more info on these design factors. 

In any case, it should be possible to achieve a transmit distance of 100cm or more with this very simple circuit and reasonably sized coils. Larger distances are possible with careful optimization.