I had the same problem as Tim T, but I think mine was because I took my 3DS into a shop for repairs years ago and they probably used adhesive when putting the top cover back on.

I had to get a pointed metal spudger-thing and slowly wiggle it into the black hinge area. Just sorta went back and forth to break up the adhesive but it worked

Ok quick edit: if you have to do what I did be careful of the area right by the top corners- I’m pretty sure there are hinges right under the cover at those spots so don’t use too much force there or you might break the plastic

I had trouble too, but got past it by slipping the bottom edge into the three indents first then easing the rest of the cover on!