1Order the PCB
Use the gerber files to order the PCB from the company of your choice. You'll also find the schematics that will allow you to modify some aspects and route your own PCB if wishes.
2Order the components
Use the BOM file to order the electronics parts from the company of your choice.
The specific parts, like the screen or replacement parts for GBA SP, can easily be found on Aliexpress.
3Populate the board
Start the soldering with the DDR2 socket. This is the trickiest part if you don't use a stencil and a heatgun.
The second difficulty is the MAX98357A IC, which is a QFN part and is easier to solder with a heatgun.
The remaining of the bottom side can be done with solder iron. Finish this side before starting the other.
On the top side, the difficulty is the LCD connector which is easier to solder with heatgun.
Resistors and capacitors are 0805 which are easy to solder by hand.
4Program the ATtiny85
Use the holes on the side to program the ATtiny85 with ATTiny_Retropie_Power-control.ino file provided. You can follow this guide to do that : https://create.arduino.cc/projecthub/arjun/programming-attiny85-with-arduino-uno-afb829
To program the ATtiny85 you'll need to first set an Arduino Uno in ISP mode.
5Flash Retropie on a SD card
Download the image on the Retropie website and a use a software like balena etcher to flash the SD card.
After that, copy the files on the SD card as follow :
config.txt -> /boot/
dt-blob.bin -> /boot/
gamepad.dtbo -> /boot/overlays/
99-keyboard.rules -> /etc/udev/rules.d/
retroarch.cfg -> /opt/retropie/configs/all/
Resize the retropie partition (ext4 FS) and create a new one for the roms (FAT32).
Move the directories in /retropie/Retropie/roms/ to the new partition.
Add a line in /etc/fstab to automount the new partition :
PARTUUID=*****-03 /home/pi/RetroPie/roms vfat defaults,auto,users,rw,nofail,umask=000 0 0
(replace ***** accordingly with the 2 first partitions)