Why do you not want to level up? Unless you're going for a low-level run through, there's no point in holding back on levelling; the monsters will beat on you just as badly as they will later in the game.

My advice is to win a lot of cards from players (without spreading the Random rule, of course), and use Card Mod to turn those cards into items, and then turn those items into powerful magic. An Abyss Worm card will get you a Windmill, which gets you 20 Tornadoes. Tornado junctions very well to HP early on in the game, and before you get past level 20 your characters can have well over 1000 HP.

Don't forget to learn HP% and Str% bonuses from your GFs as well, these will help you pretty much all the way through the game, especially the lethal HP+80%/Str+40%/Str+60% combo I have in Zell's abilites.

You will have to fight battles to earn the AP for these things. But it's also fun to watch how fast enemies fall when your characters are extra strong.