As far as I remember and according to this wiki, the difficulty level has nothing to do with the character trophy that you can get:
To obtain character trophies, players must finish Classic mode with that character. To obtain characters' Final Smash trophies, players must finish All-Star mode with that character.
So you will have 2 different trophies for each character, one for each mode. Cheking a specific trophy list from that wiki, like for example the Ice Climber trophies, you can see that there are just 2 trophies for beating the modes with that character, one for Classic and another one for All-Star.
My guess is that one of those trophies that you got with the same character was not earned just for beating that specific difficulty level, you might have earned it as a bonus trophy (beating Classic mode with X characters, beating Classic mode in less than X seconds... I don't remember the bonus ones).