Slow rise and fall on ATtiny 85v

The PNP seems to be missing a pullup resistor at its base.
I might be mistaken, but when the NPN is off, the base would float, right?
If so, wouldn't that defeat the purpose?

Also: Why do you go through all the hassle of turning the Tiny85 off and on with the external transistors?

Wouldn't it be much easier to just put it into a deep sleep mode where it would consume less than a µA? The batteries would still last years and your whole circuit would become much simpler and probably even smaller than it already is...
(You'd only need the Tiny85, bypass cap, the three buttons and your RF module.)