To put it simply, Big Bang Mini is a fireworks game and one of those games whose unique method of play could only work on the DS. Light a match and watch those fireworks go...
The premise is fairly simple. On the top screen of your Nintendo DS you have various targets. By using the stylus to "light a match" in various directions you launch fireworks at the targets. If you hit the targets when the fireworks explode, they drop stars that you collect. However you need to dodge the debris from the explosions lest you be burned.
And that's about all there is to it. It's not an overly complicated game — the hardest part that I found was learning the method to lighting the fireworks. You want to touch the stylus and flick it upwards on the touch pad very quickly and lightly. Once you get the hang of it you'll find it no problem to launch multiple fireworks up quickly to attack the targets — just watch out for that debris.
Like a lot of DS games, this one is fairly simple — but it's addictive. When I got a chance to get my hands on it and figured out how to launch the fireworks I was immediately sucked in. It looks like it's one of those great "I've got 10 minutes to play a game" kind of games. The version I saw was only about 50% done so it'll be interesting to see how it ends up.