Like in most RPGs, there's a way to power level in Star Ocean 3. First, you'll want to fill the Bonus Battle Gauge and get the '300% Exp Bonus' on it. (Keep fighting, after 15 battles with it filled, you'll eventually get every bonus.) Next, you want to get an weapon and synthesize 5 fully refined Rings of Eruditions. (20% Exp x 5 = 100% Exp, and that's the highest these factors will stack.) So therefore, a 400% Exp bonus! Go into a battle and take off all equipment from the other two characters you aren't going to control. Put everyone on Manual, and set them near where the enemies are, so that they die, eventually. Keep the person you control safe, for if they recieve a critical hit, then the BBG will break, ruining your hard work

As for killing off your other characters, this is so Exp doesn't get cut in three.
Now, equip that weapon that you refined onto one of your dead people.

Don't worry, equipment effects are still active, even if on a dead person. If you've beaten Lenneth already and gotten the Valkyrie Garb, then equip that to Nel, Mirage, or Maria, if they are in your main party. Or put them in and kill 'em. That's another 30% more Exp.
Now, if you've beaten the game, you'll want to go to the Sphere Corparation. I go to floor 186, until I find those frog looking enemies. They're slow, and easy to kill with someone with a strong wide attack. (Arbel, Vampiric Flash, Fate, Ethereal Blast, etc.) Kill them as quick as possible, with little harassment, at any rate. Bam. Major Exp. That's around 300,000 Exp normally, times four...so that's around over a million Exp. Exit the room, come back, kill the monsters. It should only take around a day this way, a few hours. Some people might call it tedious, but it's alot better than playing 'normally' and leveling up to level 255.
If you haven't beaten the game, a place like the Spiral Tower would work just fine for this, but you don't have to be at astronomical levels to beat Lucifer...this power leveling I do is usually in preparation for bosses like Lenneth and Freya. (Who I still cannot beat. ><;; )
FYI, the Battle Trophies for leveling up are:
-Reach Level 10
-Reack Level 77
-Reach Level 120
-Reach Level 255 (Maximum level.)
-5 Consecutive Level Ups
-10 Consecutive Level Ups
-15 Consecutive Level Ups
(Those are easy to get doing this, and putting and alive party member that nobody ever uses-in other words, Adlai- for one battle off to the corner with Formation, 'Escape', you should get every consecutive level up trophy. Or Souffle, or Sophia, which start at level 1

)
Ack, you may not know the Japanese names. Sorry.
Arbel-> Albel
Fate->Fayt
Souffle-> Peppita
Adlai-> Adray
Those are the only changed first names. Meh.
Meh. Sorry if that confused you. If you have any questions, just ask. But unfortunately, I don't know what item increases max HP...:/