It's Nethack on the DS. If you have no idea what Nethack is, then this is a good introduction to 'Roguelike' games
Rogue begat Nethack. Where Rogue was hard, Nethack was brutal. It required strategic thinking and serious risk management techniques.
This game is absolutely in the Roguelike family, permanent death and all. It's somewhat easier (and infinitely more accessible) than Nethack (which I haven't managed to beat in 15 years!) but doesn't compromise too much. Having items automatically identified for you when you go into town, for example, makes the early parts of the game much easier. But, for the most part, veteran Nethack players will find this very quick to pick up and play.
The critters you encounter are varied and require different strategies to defeat, especially when facing multiple foes. Often, you can manipulate them to work against each other.
Bottom line -- if you were a fan of Rogue, Nethack, Angband, Moria, or any of the other Roguelikes, get this game.