Dark Star

You have to attack the little bomb shaped creatures it spits out until they start to flash red. It will then spit out bombs for each of these flashing red creatures that will they fly up onto the top screen and split so that the bomb is heading towards either mario or luigi and the creature it heading towards the other. Just leave the bomb to bounce over you but hit the creature back towards the darkstar. Once you do this with two of the little creatures, the darkstar will sort of lose power and just sit on the floor. While it's doing this, it's your chance to deal the dammage with your best attacks, but be careful beacause after each turn it'll use a laser to zap one of the brothers (I haven't deciphered what it is that shows which one he's going to attack yet but if you jump with both then you will succeed anyway) and after two turns it'll wake up again and you just repeat the process. In theend he'll try to suck you both in but you just mash the buttons in order to run away and then it blows up.

Hope I have been of help

on a side note, The Dark star attacks who ever attacked it first. If Mario uses his turn to hit the Darkstar with, lets say, Falling Stars(if you have it yet.) even though both brothers hit it, it will go for Mario because he started the attack. And its attack, where it spins at you from the left but dissapears near the middle, Try to trace it's path, and time it by how fast it was going to counter.

Also when you get to the attack where starlow comes out grab her until the dark star fires a dark beam. When it finishes doing this immeadiatly let go of the buttons because the dark star will bounce up and get you while you're holding onto starlow