You are wasting a lot of power in your system. You need to be far more efficient when running off battery.
Don't boost your battery voltage to 5V. Instead use a system that runs entirely at 3.3V.
Never use a linear voltage regulator like the AMS1117 since it just wastes power as heat. Instead use a switching "buck" regulator.
Turning off modules when not ...
In the Arduino IDE, click on SKETCH > INCLUDE LIBRARY > MANAGE LIBRARIES.
Then, search for 9250, select the SparkFun one, and click INSTALL.
Finally, from the examples, choose the MPU9250BasicAHRS_I2C.
In the specification sheet linked to in the post we find this:
This is a very small amount of current. The Arduino ADC is a voltage sensing device and (unless modified) has a range of 0 to the operating voltage of the Arduino. Usually 3.3V or 5V.
Converting nano Amps to that range of voltage will require additional hardware. A stock ...
The Arduino Micro requires 5V. It runs at 16MHz, and you can't run at 16MHz at voltages below about 4V.
To run off a 3.7V battery you need an Arduino board that runs at 8Mhz, such as the "3.3V Pro Micro" from Sparkfun.
To know if your battery is suitable for your project you need to work out the hourly average current draw. That is the proportion of "...
The answer was, in fact, my poor experience with these boards and how they work.
As you can see in the pictures, wire and connectors are on opposite sides of the board. I was assuming that pads were connected on both sides, which is not true. Therefore, connectors were simply dead.
Soldered again at the wire side and it works like a charm. Thank you all ...