Very difficult is relative and given enough time players of most strength should be able to find a mate in one.
I don't have a concrete example, but in my view the following features would make it more difficult (some of these exclude each other):
- a large number of possible moves (i.e. lots of pieces on the board and an open position)
- the mating move is done by a piece moving to the back (towards the mating player)
- it is a non-standard mate (not one you have seen before in your tactics excercise, but rather of a studies type)
- the mating move is a move where the moving piece uncovers a piece that helps in the check mate (either by taking away squares from the king, or more tricky by pinning a possible defender)
- lots of pins are involved that prevent defenders from defending
- there are tempting moves that don't work for not-too-obvious reasons
- the move is an en passant capture or an underpromotion or castling
- (not sure this counts) the mate requires retrograde analysis to prove that en passant capture is allowed or that castling is allowed
- large distances are involved, both in the move itself and in the attacking of the king (say moving a queen from h8 to a1 to check mate a king on a8 might not be that obvious)
- the position is such that the pawns move unexpectedly in a direction you would not expect (down, left, right)
- asking for a mate in one for black (without specifying that it is black's move) This can be particularly tricky if it looks as if white could mate as well.