The truth is, the battles - the heart and soul of the game - are a bit dull, being grid-based, with ranged magical attacks. As with many RPGs, elements come into play (fire beats water and so on), so you have to consider how to attack different types of creature using different magical abilities. But not much. Truth is, you can rattle through the game applying none of this logic and still come out smelling of roses at the end.
The whole thing is enlivened a touch by the introduction of golems. Although your arch-nemesis in the game is one, golems are also used every day in the Arms world to help you out and generally... do stuff.
You can create your own golems using 'cores' that you find during your travels, each with their own specialities, and then, depending on your next opponent, you can add the most useful golems to your party and attack real nice.
Above: Don't touch it! Don't open it! Haven't you seen Tron? Idiot!