Ok, so you step-up the battery voltage from 3V3 to 5V using the ME2188
and use this directly as VCC for the ATmega328P? I never designed such a
step-up regulator, but I understand that the layout is quite critical,
so watch out for the recommendations. C3 I don't understand (but doesn't
hurt). C66 should probably be much bigger, like 4.7-100uF, or else there
is such a big capacitor missing from 3.3VA to GND. R13 is rather small,
will result in a very bright LED light shining, and might interfere with
the ISP programming; I'd rather use 1k. The ATmega328P needs two 100nF
close to the two power supplies, plus you forgot to connect pin 22 to
GND. I usually use 10k as pullup R1 for RESET, but 1k might work as
well. C4/C5 I usually use 18pF due to 2-4pF being contributed by the PCB
itself. I also prefer C33 to be 10nF instead of 100nF as this will allow
to switch the AREF source faster, but up to you. Usually there is also a
10mH coil between VCC and AVCC to reduce digital (and in your case
regulator) ripple impact on the analog measurements. Hope it helps.
Oh, one more thing out of curiosity: Why don't you use an Atmega328PB?
KR, Sebastian