This took me a couple of tries.
Don't shoot anything and don't use your bomb! You can use your boost, but use it wisely and only when desperate. Be aware, that when you boost through the green asteroids, you will get +2 seconds on your clock, which means that the total time (top right corner) is not 45 sec. anymore. (For example, when you collect the 1st time bonus, you would have to get to 47 sec., and so on.)
Take a look at the below video for an idea on how to play this mode. (credit goes out to pesico aka KittyGotWet)