I did it with Lucas the other day. A breakdown of my strategy:
Vs Master Hand: If you have trouble here, I can't help you. We've had 3 games to learn this guy's moves, and they haven't changed in any significant way, so dodge/shield them as you always would. Just use aerials, especially dairs, when hes not attacking. Best part is that his bullet shots can be PSI Magnet absorbed, so you can use his fight as free healing - just dodge his other attacks until he does that one, pull up the magnet, and watch the damage evaporate.
Vs Crazy Hand: A slightly more erratic Master Hand, but without the free-healing bullet move. A pity. Same basic idea as with his sibling, plus toss in PK projectiles when he does his bomb drop and trashing moves.
Petey Pirranah: Easy. First off, attacking an individual cage seems to do more damage than attacking his body, so pick one and keep hitting it. After the opening part, he sticks to one side or the other of the stage, so stick to the center, just out of his reach, moving as needed to avoid him when he jumps. PK Freeze when your target cage is on the far side from you, and dair/nair when it is on your side and Petey is in between swings. Should be able to take him down with no damage this way.
Ridley: Also easy. PK Freeze is good against him. Play defensively and dodge his charges, then blast him with Freeze between them. When he drags his tail along the ground, double jumping can get you a quick aerial in while he passes you by (I'd suggest dair or nair).
Meta Ridley: Keep in the air by him as much as possible to dodge his moves that slam on the Blue Falcon. Dair spam, with other aerials tossed in to help with stale move negation. When he grabs the ship to drag it down and shoot fireballs on the way, walk up to him and fsmash once or twice and he'll abort the attack. When he uses his fireball flurry, just keep in the air behind his head, hitting him all the way, and they'll never touch you. There was a video posted earlier in this thread that shows this tactic in action.
Duon: Play defensively and dodge his attacks. Keep a distance against most of his moves - the few projectiles he uses are easy to dodge, except the purple energy bolts, and those you can absorb with PSI Magnet. Otherwise he relies on jumps you'd need to be asleep to get hit with, and charges you can jump over or dodge. Toss out a PK Freeze after each of his attack sequences and abuse his absorbable attack for healing. If you want to shorten the fight, move in for some aerial attacks, but be careful, since this can give him the opportunity to use dangerous close-range attacks. You can also trick his guided missiles into hitting him, as the Dojo mentions, which can shorten the fight significantly.
Rayquaza: Your down tilt is your best weapon here. His attacks are quick though, so be careful not to get too caught up spamming it. Play defensively, find a rythym for how many down tilts you can safely get in between his attacks, then put a little distance between yourself and him and prepare to jump over or dodge his attacks, then return to down tilts. Dairs also work fairly well, if stale move negation starts to hit too hard. Also, you can get in a quick smash when he is popping up out of the ground, as the Dojo indicates. Warning: do not try to absorb his energy attacks, PSI Magnet will not work against them.
Porkey: Probably the boss I had the most trouble with long-term. Hes mobile, and neither PK Freeze nor PK Fire are terribly effective against him, so projectile spam isn't going to do it. Dair and dsmash seem to work best, but be careful of those legs, and don't get so caught up in attacking that one of his charges hits you, or you will regret it. His mini-bombs should be easy to avoid. The lightning bolts he sends your way you should try to air dodge or roll against - I haven't found a way to avoid them entirely, but minimizing their effect works nicely. When he jumps into the air, just run from side to side, and make sure you're not in his spotlight when he drops his lightning bolts.
Galleom: Another pain-in-the-*** boss for me. He seems to be vulnerable to ice moves, and this holds true for PK Freeze, so toss them his way whenever you can. Otherwise, basic aerials are also good, particularly fair and dair. Play very defensively though, as any hits from him are dangerous, and be especially careful to avoid his uppercut punch. Vs his jumps, air dodges work well. Vs his spin and body slam attacks, back away and punish him with PK Freeze. When he fires his rockets, rush into point-blank range to avoid them, and smack him with an aerial or some tilts while you're there. When he goes into tank mode, watch for a second to see if he deploys rocket launchers - if he doesn't, jump over him to avoid his charge; if he does, get in close and use dodges to avoid them.
Tabuu: If you beat him in SSE on hard or above, you can definitely beat him here. The main thing to watch out for is, of course, his Red Rings of Death - they're still instant doom if you get hit by them. Spot-dodge those, and you should be golden just by evading his other moves and tossing aerials his way between attacks, PK Freeze/Thunder when he does a move that leaves him vulnerable (for instance, when he does his close-range finger-slashing move and you manage to get behind him), and when he does his eye-beam attack get up next to his face and punish him with fsmashes.
General Tips: As if I didn't say it enough before, play defensively! This is an endurance test - get in a few hits, wait for the boss' attack to make sure you're able to dodge it, then resume attacking after you do so. Don't go all out hoping to end the fight as quickly as possible. PK Thunder may be tempting to spam, as it is an effective weapon against many bosses, but don't - it leaves Lucas too vulnerable. It can be a good finisher when they're at low hp, though. For heart containers, all I can say is use 'em when you need 'em, treat the Master Hand fight as an extra one, and try to save one for just before Tabuu, so that you have room to make errors against him if need be.
Hope this helps someone.
Edit: You know, looking back on it, I'm beginning to suspect that each boss may have weaknesses and resistances to a specific types of attacks. I know that PK Freeze seemed to do unusually large amounts of damage to Galleom, and when I did the Ice Climbers on easy, he absolutely melted to their Blizzard attack, far quicker than is normal even on that mode. Meanwhile, Rayquaza and Petey seemed abnormally resistant to PK Freeze, and Rayquaza in particular seemed to take less damage from all of Lucas' attacks than the other bosses did, except for down tilt only, which is different from the others in that it doesn't have Psi hexagons attached to it. Perhaps each boss is vulnerable to one of the different attack types that the stickers list - cold, electric, energy, slashing, bludgeoning, etc etc. That would explain a lot. And perhaps make this easier on everyone, if we could discover the weaknesses and resistances on each.
Zevox