It would be hard to pull off well... though it's fair to point out that it's difficult to pull off anything well. XD
I mean, given the way this game plays I could only see one way of making it hard (and correct me if anyone doesn't agree):
HARD MODE:
-Scale all regular enemies' level to approximately x1.3-1.4 of Noct's level
-Scale all bosses to x1.5-1.7 of Noct's level
-Adjust the experience needed per level to be higher (so you level up slower)
-Make hourly cooking cooldowns for Ignis (crazy good dishes need longer cooldowns on Iggy before he cooks again)
-Adjust the frequency of finding potions to very low in the world (and heavily nerf Galdio's survival skill)
-Increase the prices of restorative items in shops (eg: make a potion cost 1K, so 10potions=10K, which is good since money is not easy to farm)
-Make a custom tutorial for Hard Mode that stresses the timing of blocking (block just in time = restore health partially etc)
Results:
>Higher level-scaled monsters at all times and slower leveling will prevent you from being overpowered
>Less potions in the world with high shop prices will never result in potion spamming (since it'll be a limited resource)
>And a cooldown on Iggy cooking crazy foods will balance out the insane food buffs that break the game
>The new stress put on the player will have you timing your blocking to restore HP/MP, switching characters to keep distances in tight situations or having the switched character tank some hits while the other party member slowly restores health (so rather than potion spamming, you change character to have the other heal)