When you're playing through the little fortressy levels of Super Mario Bros 3, you come across a miniboss, Boom Boom. A lot of people have trouble with him for some reason, but he's actually a giant pushover with the right technique.
You have to stomp on him three times to do him in, and he varies his attacks by flying around or leaping across the room or whatever. All you have to do is time your jumps so that you land on him at the exact moment he recovers from being stunned. That way he doesn't even get to use his Crazy Attacks and you finish him off in just a few seconds, like this video demonstrates.
Making the boss room trigger a sigh of relief instead of inducing mild panic.