Unlockable Character
You can unlock the character Curian by completing Celine's mission on at least normal difficulty. You don't have to actually finish the entire game, but you must beat the boss Encablossa and you will be able to unlock Curian when you choose a new game. Note that Curian doesn't actually have a quest, unlike all the other players. Instead, playing as him allows you to see deeper background information of other players.
Higher Difficulties
There are two more difficulties in the game above the Normal level, and you unlock each one by beating the previous difficulty. So to get Hard difficulty, beat the game on Normal difficulty, and to get Extreme difficulty, defeat the game on Hard difficulty. It does not matter which character you use to complete each difficulty level.
Potion Synthesis
Combining potions with different items can produce different effects. For example, combining an orange potion with a weapon will increase the attack power of that weapon, and mixing a blue potion with an armor will increase your hit points and thus your defense. If you use a panacea with any item, you will automatically eliminate any negative effects of a cursed item.
Rare Items and Enemies
You can find rare enemies and rare items by adjusting your difficulty and utilizing luck more. First, adjust the difficulty level to hard or extreme. This will make the rarer enemies come out more. Then, while in battle, use a yellow potion on a character with a high luck level just before defeating the enemy. This will make the rare items drop a bit more often.