Faster Unlimited Heartless Battles Without Map Cards

If you do not wish to(or cannot) use False Bounty, then try this. Warp to the entrance room of a world from a different floor, and there will be Heartless there. Defeat them, then warp to a different floor. You may repeat this as many times as desired without using a single Map Card.

Heartless battles without Map Cards.

In order to have unlimited battles with Heartless without wasting your Map Cards simply save your game. Then use a False Bounty and open the 2 chests that contain Heartless but always leave the one with the treasure close. Once you've fought the 2 Heartless chests, get out of the room and re-enter, both Heartless chests will be close again for you to fight them again.
Repeat this process as many times as you want to level up without using any extra Map Cards.

Premium All Your Cards Fast (or semi-fast)

Similar to the Moogle Points trick, you'll walk between two rooms over and over, and this trick depends a lot on luck.

The requirements are that one of the rooms is a Premium Room, and that that room has to have a BARREL in it. So, once you've cleared the room of enemies, just leave and come back. The barrel will respawn each time, and whenever you break it, you will either get health, moogle points, or, if your lucky, a barrel spider. Get it? The spiders respawn (with luck) and thus your chances of getting a Premium Bonus are high. Even when you don't get spiders, this will help you get Moogle Points.

This certainly takes a while, and I wouldn't recommend trying to do it to your whole collection. When I did it it took me about 30-45 minutes to premium about 20-25 cards. That's pretty good, and it helped a ton. I also got a few thousand moogle points, so that helped to.

I recommend making a deck of high-CP cards that you commonly use, especially stuff like Cloud. Barrel Spiders all have an attack power of 4, so keep all your cards above that and you won't have any trouble. It's tedious, but it really can be worth it.

Skip pre-boss fight conversations

If you've lost to a boss fight and get tired of listening to the conversations that take place before the fight press start and hold it down for a few seconds and the battle will begin. This becomes very helpful in tough boss fights where you are constantly restarting over and over