My god, that level was hard. I'm assuming you're not having trouble with coin 1, but here's what I did for the other two:
For coin 2, stand to the left of the coin, just far enough to the right that the piranha plants below you can eat away at the ice above the coin. Staying to the left keeps the mass of piranha plants to the right dormant so they don't destroy your exit bridge. As soon as you have an opening, jump down there, nab the coin, and run like hell to the right before the other piranha plants have a chance to melt all the ice.
For coin 3, fall down into the gap as soon as you get a chance, and wall jump back and forth until you're all clear up above. Do a midair spinny move before landing on the top of one of the walls to slow yourself down.
In general, just pretend you're doing one of the super skills videos. Run fast and do a lot of spinny moves to maximize air time. The piranha plants are easier to get through if you don't wait around for them to fill the screen with fireballs.
Speaking of spinny moves, I was playing the old New Super Mario Bros a while back, and I kept accidentally shaking the DS trying to save a bad jump.