LDO requirement for battery powered micro-controllers
I just answered a similar question: Choosing a battery based on requirements and circuit&#39;s voltage

To achieve really long battery time, you need to shut down everything except some electronics with tiny current draw that wakes up the system based on your choice of event. This could control the regulator shutdown pin, making quiescent current of the regulator and other parts irrelevant.

If RF needs 2.2-3.3 and no other parts require 3.3V or higher, you're best off using a regulator of maybe 2.5 V output, as atmega can run from this voltage when using a low clock speed. Lower voltage means lower current consumption too for many ICs.

It might or might not be advantageous to use a switching regulator to avoid wasting the power of the excess voltage when going from ca 4 down to 2.5 V, for the times when the circuit is active. Look at efficiency and quiescent current for the switching regulator at the load current that you expect.

Kevin Darrah explains how he solved a similar application. You can look at his TrigBoard here https://www.kevindarrah.com/wiki/index.php?title=TrigBoard or on Youtube.

Low-power design is fun -- and time-consuming.