I think a good general strategy for this game would be to go all-out offensive and manipulate Close Call, Lucky Day, and/or Pretty Lucky to never take damage. Then you could concentrate all on attack and never have to worry about defense. The best way to do this (assuming enemy misses can safely be manipulated in almost every situation) would be to have Mario in peril (1 hp) the whole game and reap the benfits of the Mega Rush badge, which increases Mario's attack by 4 for only one badge point. The bagde isnt found until Tubba Blubba's castle, but before then a different strategy could be used.
The following badges are badges that would help with this strategy by boosting offense and luck of enemies missing whenever possible:
All or Nothing (4 bp) - Bought at Rowf's Badge Shop after Chapter 4 (100 Coins) - Mario's attack power will go up by 1 if he successfully uses the action command. If not, his attack power goes down to 0.
Close Call (1 bp) - Goomba Road - When HP is 5 or lower, enemy attacks fail 1/4 of the time - this should be able to be manipulated to never take damage during the run
Lucky Day (7 bp!) - Received from Goompapa after the letter trading sequence - causes some attacks to miss regarless of HP - would make Close Call manipulating easier maybe?
Mega Rush (1 bp) - Tubba Blubba's Castle - When Mario's HP drops really low and he's in "peril", his attack power goes up by 4
Power Bounce (2 bp) - Koopa Bros. Fortress - For 3 FP, Mario can bounce on an enemy continuously until you miss an action command - this would be great for boss battles early on before you had a lot of power, bosses could be defeated in one turn with tools
P-Up, D-Down (2 bp) - Crystal Palace - Your attack power goes up by 1, but your defense power goes down by 1 - a nice alternative to Power Plus, since defense doesnt matter anyway
Power Plus (6 bp) - Shy Guy's Toybox; Traded by Merlow for 25 Star Pieces - power goes up by one (2 if you wear both)
Pretty Lucky (3 bp) - Traded from Merlow for 5 Star Pieces - alternative to Lucky Day
Speedy Spin (1 bp) - Bought from Rowf's Badge Shop after Chapter 1 (50 Coins) - spin dash goes futher and faster - this is a must
Spike Shield (2 bp) - Dry Dry Ruins - Allows Mario to safely jump on spikey enemies without getting hurt
None of theses badges except Power Bounce require FP, so most of the upgrading could be used for Badge Points. Health should never need to be upgraded.
One thing to consider: Mario's base power with the Ultra Boots is 4 when you first hit the enemy (an action command hits twice and makes it 8). The badges above increase this Power by another 8 (AoN 1, MR 4, P-up 1, PPx2, 2). So now Mario's base jump damage is 12 (24 with action command). If you use a Super Jump Charge (4 fp, 2 badge points, Bought from Rowf's Badge Shop after Chapter 5 (100 Coins)), your jump power goes up by another 3, making it 15. If you then use a Power Bounce, Mario's attack will be 15+14+13+12+11+10+9+8+7+6+5+4+3+2+1+1+1+1.... which gives 124 damage! This is the most exaggerated case, and you probably wouldnt have Super Jump Charge, but this just goes to show how you could easily defeat any boss in the game in one turn.
With the boss aspect taken care of, we now have to consider enemy battles. The vast majority of random enemy battles can (and should) be avoided. This means a minimal amount of level ups, but level ups are not really needed. The only thing they're needed for is bp, since hp will always be low and fp will only be needed for Power Bounce in the boss fights. The badges listed above dont really require much bp at all: Lucky Day and Pretty Lucky are probably not necessary at all, and the Power Bounce badge need only be equipped for boss battles. If Mario is at a low level when he reaches a boss, bosses will give him tons of star points, enough for one or two level ups each, which would be more than enough for the suggested badge combination, especially because many of these badges arent available right away so there'd be time to level up from bosses before reaching these badges.
If there are some unavoidable battles that arent "boss battles," you could just use a Fright Jar (which gives no star points but oh well) on them (only 5 coins at Shroom Grocery). Fright Jar isnt guaranteed to scare away all enemies, but this could probably be manipulated to work. If you absolutely have to fight an enemy and a Fright Jar wont work (very unlikely), itd be very easy to kill them without using fp or even letting them have a turn in most cases. Baisc strategy: if there are 2 enemeis, Mario attacks one, partner attacks the other, done. If there are 3 or more enemies: Mario attacks 1, partner attacks one, remaining 2 enemies attack and miss, Mario and partner take turn 2 and finish battle. Better strategy: if there are 3+ enemies, kill them all in one turn by option A: sacrificing some fp and using a move such as Sushi's Tidal Wave, any of Koopers' attacks, Quake Hammer, Multibounce, etc. Or, since we wont have much fp, the better option B would be to stock up on Mystery bags in Boo's Mansion (only 1 coin each). Then manipulate these mystery bags to be a Thunder Rage every time, which does 5 damage to all enemies. If the enemies have more than 5 hp, you could use double or triple dip to do 2 or 3 Thunder Rages, do a parter ability that attacks many enemies, or use Star Storm. But there wont be many required non-boss battles that a Fright Jar wont work on.
So the way I see it, do a damageless run using maxed out power. Avoid all possible battles since they cost time and you dont need to level up much. Use maxed out Power Bounce for boss battles, and use the level ups you get from them to supply bp, never needing to increase hp of fp. I think this would be the best overall strategy. Thoughts on this?
Is anyone thinking of doing this run? I could help make it or just contribute strategies or whatever is needed (I dont think I could or would want to do the whole thing by myself). This would be a very awesome game to TAS and I'd love to see a run of it. :)