Well, it is turned based, but what makes it a bit more engaging is the grid system. The battle takes place on a I think a 3 x 6 grid, you're on one 3 x 3 and they are on the other 3 x 3. When one is in the row closest to front, they do more damage but they receive more damage, and further to the back they do less damage but they receive less damage from attacks (which makes it a good place to put your healers and other support characters)
Each character also has various skills which allow you to do damage while shifting the enemies around the board, stack them as many on one tile as possible through the various push, pull, and slide attack skills, then unleash your strongest attack to hit all of them. This is later complicated by enemies which can't be moved, shield spells which protect enemies standing in certain rows/columns, etc, to keep it from getting stale.
You also have the capability to give your turn to one of your characters or even exchange your turn with an enemy's so that you can have more turns in a row to herd all the enemies together and hit them all at once, as once your string of turns end, the enemies move off so there is only 1 per tile again.
Basically it has some of the strategist aspect of an RTS, while not actually being in real-time so you have plenty of time to plan your string of attacks.
The story is also quite engaging and the time travel mechanic is quite well done as you shift back and forth between 2 alternative history timelines with the ultimate goal of saving the world by using the differences between the two timelines to solve problems in the other timeline. Each of those 2 timelines can branch off in other different directions and result in dozens of different endings (both game ending and good).
What's nice is when you hit a bad ending, your not done, the time travel mechanic kicks in and takes you back to the last available node (there's usually a node for every 3-4 events in the timeline). Using the time travel mechanic you can freely jump around to any node in the timeline to replay a section so you don't ever have to worry about missing anything. It also means you don't have to replay the entire game over several times to see every ending.
Here's a good example of the mechanics of battle: