Don't just pick up power-ups willy-nilly. Get used to which icons provide which abilities and make a beeline for those when they drop.
Be careful not to get stuck as the scenery rebuilds - keep blasting ahead of you to clear a route forwards.
When carrying the football, don't worry too much about shooting enemies - just try and stay out of their way.
Watch for the arrows that show you the direction of nearby enemies - you can shoot off screen to kill them if you don't want to risk getting any closer. This applies for bosses, too.