There is no leveling through battle similar to chrono cross. The only way to level is through bosses. I chose this method to maximize strategy in the game. You can't simply powerlevel (though you can grind to get better equipment and skills) to get through a rough spot. You will have to more than likely employ a viable strategy and execute it to defeat many of the tougher fights later in the game.
Random battles are still important as they will yield materials, gold, and jp. If you simply go from point A to B and fight the boss you are missing out on potential loot that could be vital to crafting a piece of equipment that you will need later. Still it is entirely up to the player how much they want to battle. I tried to the make battle system as swift and painless as possible. It isn't very complicated but I implemented a boatload of states to keep everything fresh.
I am thinking of implementing a hunts board for Akuma a la final fantasy 12. I feel it would be a interesting thing to add in the future.
Puzzles will be simple for the most part except for in a few cases. I want the focus to be on the gameplay/story and not how much I can outsmart you in a dungeon. I would much rather outsmart you in battle.