According to posts like the one here, all you need to do is defeat the final boss on Hard mode -- you don't even have to play through the whole game on that difficulty.
This is more easy than it looks, if you already knew all the paths and what to do, it's easy and can be achieved quickly, you just need to look at your life, since the hourglass keeps stealing it.
There's an easy method and it can be achieved using the password system. In the main menu use Triangle to input this password:
MJWH WC5 TY3B XJR
You'll be at the end of the game with all itens. Just equip the Legendary Sword, the Heavenly Shield and the Legendary Armour. Since the Hawk-Man has the ability to fly, keep pressing X and fly to under the platform left to the tower in the village. Under that and under the door is a hidden door you can acess pressing Up. Buy 3 potions and the with the rest of the money the Thunder item. Now exit and fly to the most left side of the platform. On top of it, it'll be a hidden door, press Up and you'll be at the very end. Enter this last door and defeat the Vampire Dragon. It's not that difficult, you just need to hit him on the belly. Since you have 3 potions you can "die" 3 times trying to kill him
A video of this method can be seen here: