Support characters that belong to friends will have access to additional attacks they otherwise wouldn't possess.

You can find special equipment when in Vortex. You can also earn extra HP. Limitations are that you can only unlock a single dungeon per day.

Side quests will earn you special prizes, equipment that you cannot buy in a store, or a crafting recipe for a new spell or rare piece of equipment, or even to synthesize a new character.

Hit 'optimize' in order to automatically equip the best equipment for your character.

Shop around as much as you can. Shop for potions and characters. In both cases having a lot of them increases your chances to survive powerful attacks.

Limit breaks are powerful attacks but they can use you up fast. Think about saving them for situations when you need to inflict a lot of damage in a hurry. Don't waste it.

Watch out for special characters: Metal Cactaur is useless in battle, but if you use it as a sacrifice when you enhance a character, it will give that character 10,000 EXP in one shot. Gil Tortoise can earn you 10,000 Gil when selling.