Although there was no need for me to do so as my charging port worked, I converted my Gameboy Micro to USB C. In 2021 I'm on a mission to USB C everything.
Pre warning: I do this as a hobby. I'm not Nintendo. I'm not an electrical engineer. If you break anything it's not my fault.
What you need:
Soldering iron + solder
6 pin female USB C
Flux (not a must, but always a help)
Tri wing and phillips head screw drivers
Thin wire (I use enamel wire 25G, any thin wire will do)
Hot glue
Disassembly. iFixit rates the Micro as a high difficulty teardown. Follow their guide, they're the pros here. The start select buttons are attached via a very delicate flex cable with no connectors. Take extreme care, don't be dumb like me (I ripped it).
Remove the original charge port. This is best done from the back side of the board. I used flux and hot air. You can also use extra solder to heat all the pins at once, use a desoldering pump or desoldering/copper wick.
Once desoldered, the following pins must be attached for + and - Choose only one spot for positive and one for negative.
Connect the wires to the corresponding pads on the board. I then like to strengthen the wires by using a tiny amount of hot glue on the joints. I then add hot glue to the bottom of the port and use a male USB C cord to position the port while the glue is hot. Make sure you line it up so the female and male port can connect without the micro shell getting in the way.
That's it. I made no cuts or trims when completing this mod.
I initially followed this guide which you can also have a look at for other pictures, although it uses a micro USB.
*** I recommend using USB A - C chargers only with this mod