This achievement can be a pain if you go into it unprepared.
You see,the problem is you win the expert cup by getting a podium finish (1st, 2nd or 3rd) and the cup looks the same for every finishing position.
So i suggest as soon as you unlock expert difficulty and are ready to tackle Expert GP,start on the first GP and keep playing it until you place 1st on the podium.
Or at the very least write down the ones you have come 1st on,or you will find yourself replaying them over an over trying to find the GP you need 1st on.
Yes,this did happen to me and i got very frustrated and cursed myself for not making a note in the first place.