I can't comment more right now, but you should be using Force almost exclusively compared to Fire (it's supercharge owns everything, period), and you need to use down-a more too (pink and the three pillar guys in 2-2, specifically).
[edit]alright, I definitely plan on running this for SDA. I've had a couple demo runs posted
here, but both of the links are defunct and I lost the files.
Alright, first, did you try down-a sliding and then jump-kicking for fast movement as opposed to jump-kicking?
Are you sure that Fire (weapon 2 for red) deals more damage normally than Force (weapon 1 for red) for their uncharged shots? I use Force almost exclusively because it's supercharge is far far far more useful. It regenerates itself if you hit stuff - it'll never run out. Fire's supercharge is one-use only. Besides that, there's lots more things you can use supercharged force for than fire, for whatever reason.
For 0-2, right before you meet general gray, you can just jump over the spinning guy and go right through the door. You don't need to jump up and go through the crate room.
1-2, use supercharged force on the plant thing that rises up. I'm almost sure that's faster.
Can't say anything about the save-the-chicks part, I always sucked on that.
1-5, pink can be defeated much quicker by standing next to her (on top of her robot, next to her actual body) and down-Aing into her and releasing supercharged fires.
2-2, you can kill the three pillar guys about 3x quicker. Don't hang from the wire. I can't remember the exact details, but you have to move to the center of the battlefield, then jump left past the leftmost (to prevent them from hiding in the ground too soon or some such, I can't remember, and you can optimize this better than I), then down-A them.
Orange can be defeated 5x quicker by hopping onto the edge of the plane, getting him to rush you, and then jumping over him and using supercharged Force on him. If the plane is against the edge of the map, he'll simply get stuck there from getting bounced back against it and you can kill him in 5 secs max.
Stage 3 I'll be looking to you for. The only thing I did was supercharge fire the train and then supercharge force the boss. You definitely want to luck manipulate the urchin form in there for the fight against seven force (it takes damage super-freaking-quickly), and there can either be A: no direction changes (ie, the battlefield must stay completley horizontal, you can't switch directions and start moving up) or switch ONCE only. The battlefield will have to switch once simply because it does at the end if you're not heading up already, but any more than that is a waste.
Stage 4, best dice palace route is 4-3-1-1-5 afaik. The first roll, minion soldier, can be defeated easily by holding left as you enter the room. He'll do his green slice attack towards you. Get hit by it at the edge of the map, then turn left and smite him with the sword a few times.
For 5, you can skip the text where gray demands payment of gems.
For G-ARC, supercharge force pink, slide into orange once and then supercharge force him, and luck manipulate Green so he does nothing but urchin form. And have fun with golden silver, I hate that fight.
These strategies can probably be improved, but they're a decent starting place regardless (I hope, anyways...).
[minor edit]kind of pointless, but you can skip the power-on company logos and so on by soft resetting (start/select/a/b-ing) the game asap and then hitting start.