I struggled with it until I figured out how it worked...
In case you don't know (and chances are most people are smarter than me and figured it out) the box the name is in reveals the grey section behind it. So if it breaks on a part of the picture that isn't covered it does nothing for ya.
As for some general tips...
Prioritize hard sections:
Sometimes, there are a some moving horizontally across all parts of the screen, other times vertically across all parts of the screen. Sometimes however, there arel only be two column moving vertically with nothing crossing the center.
The picture itself also moves. (I suspect, though am not 100% sure it does this when credits are being hit.) The game will start with the bottom covered, and the picture moving up. It will eventually go down below the standing platform again.
Because of these, prioritize the bottom and center over most else when the chances are there. There are fewer chances to hit those areas than the rest so get them while you can.
Pick a character with some quick tilts, and ariels, that are already programmed to your instincts.
Items:
I like the Smart Bomb... if I can toss it into the middle of a large grey area while credits rush past it a lot is cleared. Downside though is if it lands wrong the outer part of the explosion will break credits wiht no revealing that could have been used.
X Bomb I have used if the picture looked like it may help, or I was trying to quickly move it... but this one is much harder to control.
Screwattack: Avoid this garbage... maybe others can use it but I hate it. Messes to much with jump height and attempts to throw out air attacks... but if you are good with this item then maybe it would help.
Mushroom: Good item as well, long as you can use it right. If it is going to make it harder to get that last spot avoid it, but if there is a mess of grey and uptilting to clear a bunch looks good grab it.
I don't know if you are trying to achieve this for the sake of achieving it, or just for the reward. (This isn't a judgement, games are supposed to be fun and if you don't find it fun then why do it the hard way?) If it is the latter, bring a friend along through 2 player classic. Assuming he cooperates and doesn't try to hit you, then it becomes significantly easier.
Good luck... and at least with me it always takes a bit of that.