In City Trial mode, there are several events that happen where you can do something to gain lots of powerups. Here are some of them:

When the giant U.F.O. comes, go to top of the volcano and cross the bridge, entering the volcano. You will be lifted to a sky tower high above the city. When the U.F.O. flies below the sky tower, drop down onto it and you will find several powerups.

When the giant pillar comes, just destroy it, like it says to.
Whenever Dyna Bird comes, she is always near a ramp. When you have the ability of flight, fly off the ramp and hit her head. Once you've done that enough times, Dyna Bird will fly away, leaving behind many items.

Whenever Tac comes, run into him to make him drop items.