Use the flat end of a spudger or your fingernail to flip up the retaining flap on the speaker assembly ribbon cable ZIF socket.
Be sure you are prying up on the hinged retaining flap, NOT the socket itself. Damaging the socket or cable will result in a 3DS that will blink its power LED when you press the power button - and do nothing else.
Disconnect the speaker assembly ribbon cable with a pair of tweezers.
Continue lifting the motherboard assembly and rotate it until it is resting next to the rest of the device.
Use the flat end of a spudger or your fingernail to flip up the retaining flap on the LCD ribbon cable ZIF socket.
Be sure you are prying up on the hinged retaining flap, not the socket itself. Damaging the socket or cable will result in a 3DS that won't have a functional top screen.
Starting at the bottom right corner, insert the flat end of a spudger between the touchscreen and LCD frame and gently pry the touchscreen off the LCD.
Do not run the spudger down the side of the display assembly to loosen the touchscreen. The two components of the display assembly are held together by a fairly weak adhesive tape, and running the spudger between the two could tangle or damage the tape.
Insert the spudger into the top right corner between the two pieces and pry the touchscreen off the LCD frame.