In some previous versions of Smash Bros. you could tell how many continues a character used based on the final digit of the score. Also the color of the Smash icon used to signify the highest difficulty you actually beat the game on.
Unfortunately this version changed that formula, plus the difficulty level on the character select screen is misleading, since it only indicates which difficulty level your highest score was on. You can now very easily score higher on a higher difficulty level without completing it in this version. As a result, it becomes more difficult to tell just at a glance. Thankfully Classic mode is much easier to hunt down which difficulty levels you beat with each character, compared to All-Star mode.
Just select each character, one at a time, press start, and look for that character's icon on the screen where you choose your difficulty level. That screen will give the true answer to which difficulty level you actually beat the game on with that character. Then you can exit back to the character select screen and repeat as often as needed until you've hunted them all down.