Carefulness to the extreme is my only tip. Nothing in particular is really difficult, but there are a lot of small, sensetive parts to take care with. Such as the reset button, sound wires, screen area, etc. Make sure to not work in a place where dropped items easily gets lost, such as over a fluffy carpet or anything. Screws are dropped easily for one...
Also, if mixturing with the screen part, make sure that there is no dust or dirt between the screens or on the background plate when you screw together the tamagotchi again. Dust can be difficult to spot while working, but often clearly visible and really annoying afterwards when playing with the tamagotchi...