Sonic Rush isn't really that hard of a game, but you will run through lots of lives. This is mostly because Sonic moves at Ludicrous Speed and if you're not expecting a pitfall (which you won't your first few times through the stages) you just can't react fast enough to avoid it. The solution? Throw more lives (a.k.a. chances) at the problem. But, Sonic only starts with three lives. That's a problem.

Or is it?

One of the neat things about this game is that it allows you to go back to stages that you've already beaten to get powerups, like Chaos Emeralds or extra lives.

You should be able to complete the first stage pretty easily, since it's kind of the intro to the game. Along the way, you'll be able to pick up 100 rings with little effort, the stage is loaded with them.

Once you have your 100 rings (which, after running through the stage a few times shouldn't take more than about 45 seconds), assuming you've already cleared the area, you can just press Start and then choose to leave the stage, and you get to keep the lives you got. Just rinse and repeat until you have as many lives as you want.

You'll notice, though, that the counter in the bottom-left corner stops at 9. You can get way more lives than that, though. They show up on the Overworld map screen.