Avoid the walls at all costs
You may have already found out about this, but, the tunnels are not your friend. These tunnels have walls, and if you bump into them then it's game over. The tunnels can be attractive, as they do have some rewards for you, but your precision will be tested.
In many games like this, bouncing off the walls can be advantageous but not here, unfortunately. If you feel like you can avoid the walls, then go for the tunnel and grab the diamonds. If you don't feel comfortable going through them, then get a good jump on the ramp and land on top of it.
Of course, when on the roof of the tunnel, you need to make sure to stay on it and balance a bit. Because aside from tunnel walls, you can most definitely fall off the map. So tread carefully and think fast in certain situations on the track. You'll get used to it once you make it through a few tunnels. It's a tad tricky, but very far from impossible.
Use the booster
If you have a need for speed, then there's a booster feature that you can activate in the main menu. This will allow you to go a quicker rate through the tracks. Your reaction times need to be a bit faster, but aside from that, it's a good way to finish a level faster.
The catch is that you have a time limit for how long you can use the booster for. Usually, it's about three minutes from when you activate it. So be swift and take advantage. You may be able to squeeze in three levels with it active if you don't fall or hit a wall.
You will have another opportunity after it's over though so don't worry. Just make sure you have enough diamonds on you. The first time you do it, it's free though so make the most of it. Getting through levels as quickly as possible allows you to avoid mistakes and that's not a bad thing at all.
Customize the ball
It will take a few playthroughs to really unlock, but you can earn some new looking balls to use for your runs. This is actually done by creation, as you can usually put a couple of balls together to create one new, shiny, designer ball.
There are plenty of cool styles to unlock and you just need to keep playing and advance through levels. The good thing is that each one has its own control rating. Naturally, the rarer the ball, the better control that it possesses.
So if you really want to avoid falling or hitting those deadly walls, then you definitely want something with great control. Also, there are times where a platform may catch you off guard when jumping. It might be on your left or right, forcing you to quickly shift in that direction. Having a ball with great control can be very helpful in that regard.