Try everything! This game gives you a million ways to experiment. If you hit a wall, change up your strategy!
To get the maximum amount of character development in the least amount of time: use every type of skill. Each skill type (fist, sword, magic, etc.) improves a different set of stats and unlocks a different branch of abilities. If you use every skill type you've got at least once per battle, you'll become a powerhouse in no time!
Don't neglect the "Punch" skill. It's the key to unlocking some of the most ridiculously powerful skills in the game (not for Witches or Droids though)!
The "Guard" function will increase your Attack stat x3 for the next turn.
The Bazookas are a crutch for when you're in a pinch, but relying on them too much will lead to having really weak characters!
There is a secret character who doesn't look like much, but has a kind of magic that nobody else does. This magic is stupid-powerful - he can learn a spell that can take down most bosses in one hit. If you're really sick of these bosses, maybe hunt around for this secret character instead...