You can do this once you are on "Energy Nede" after getting the Psynard. Then you will be off to clear the four fields of test. Right below the center of the map there is a floating island called the "field of love". I suggest you have leveled up a bit, before going there, because there are some really hard monsters in there, especially those mages that disappear when moving. Those are really hard to kill. but while on that field you will sometimes encounter those jello looking things with some type of sphere in the center. Its good you come across these monsters often because they do give much experience when you kill em.
Before you go into battle with these monsters though, you will need an experience card.You can create one using the art item creation with magic canvas. That is what I did, so, then after you can replicate it using a magical camera or ririca(best of the two) and magical films. It is best when you have a character that has level up the replication skill.
O.k. once in battle, make sure your characters are set not to attack the enemy. especially not with magic. (take note that you will need someone in your party who is able to use symbology). You can use anyone in your party to do physical attacks, and most likely they won't do much damage to the jello looking monsters. You will see they start to duplicate themselves. not to worry, they do not do much damage either. You will want them to duplicate as much as they can. But I think there is a limit on how many times they can do this per battle. You will notice they have reach their limit on duplicating when you try to attack them, they try to duplicate themselves for a split second, but go back to normal. It's a good idea to use the experience card after that. Now you will need someone to do magic spell, like Celine. Do thundercloud or similar magic that will damage all enemies. Just make sure all characters in your party are away from the enemies, because sometimes the jello looking monsters explode after they receive magic attack,and lots of poison bubbles generates from them. If you take more than 2 you are in trouble. (of course you want all your party members to be alive when battle is over, so they can get credit for the experience received).
Once you have killed all the monsters you will receive 309,400 experience points(154,700 if you do not use the experience card). It's is the most I have ever received in just one battle. You can do this over again and level up fast, and get lots Skill Points(SP) too.