I don't expect this guide to be as in-depth as possible, but it should build on what I've seen here on Steam. If you want something added, or disagree, feel free to tell me.

*Spoiler alert*
I'm assuming the player has already achieved ultimate power, and understands how the philosopher's stone works.

As the game starts, hold the jump button, to charge up all five bars. Keep holding jump for about 2-3 more jumps to use the one collective. This is the fastest way to charge up one collective from scratch, and can be used repeatedly at the start to charge up the philosopher's stone. Naturally, it's recommended to use one collective as often as it is safe, even if it gets a bit repetitive. As long as it's enough firepower to keep the robots at bay, there is no need to let go of the jump button between collectives.

It should also be pointed out that as easy as it is to collect record pieces, they should be left on the field for strategic use. Any use of Savant's chain actually grants temporary invulnerability, as signified by his sprite blinking in and out of the screen, like in pretty much any sidescrolling Gameboy Advance game (I can't help but think of Kirby). This includes one collective, and picking up record pieces. For this reason, I advise to leave the pieces, and press Q when you think you'd otherwise take damage. They come in handy when fighting five or more wyrms at a time, or when you just know you don't have the firepower to kill everything before getting hurt.

On the topic of firepower, Savant's basic attack is more effective when the five-burst is used strategically; instead of just holding down M1, letting go and re-clicking the mouse button when switching to target the next group proves to faster destroy enemies.
To add to this, I find that it goes even faster when roll-dodging. Now, with an empty philosopher's stone, I'm not sure if rolling is actually faster, because I didn't actually time it, and while there is a shorter delay from the "attack start" sound to the actual attack, I don't know if it's still faster when accounting for the roll time. I'm afraid it might just feel smoother at first. I can say that it is almost always slower when using jump, though. Now, when filling up the philosopher's stone, it will definitely become more effective, and even without it, there are still times it's more effective to dodge; when a group of fodders is on the other side of the map, and rolling would move Savant closer to them, his proximity to the enemies makes the attack burst more effective, in that the projectiles reach faster, and the full burst is almost sure to hit the mob (I can't vouch for your aim). Combine that with the fact that every dodge helps charge up the secondary/one collective/double damage, and you can see the effectiveness.
Regardless, there will still be times when it's more effective to just click again, mostly because the mobs of most immediate concern will far on one side, and the increased distance from a roll will lessen the effectiveness. These instances will eventually disappear with a charged philosopher's stone, as the speed of the roll will be so fast that rolling away and back will be more effective than waiting that half-second to reset Savant's basic attack. On the other hand, the philosopher's stone will give such increased attack speed, that at times it can be more effective to just hold the attack, instead of resetting it. It's up to the player to find when each technique is more effective.
A final note: rolling most definitely feels smoother; you could spend a weekend in a freezer, and still never have felt cooler.

Moving to the topic of wyrms, the best advice I can give is to make sure you have your secondary attack ready by the time the wyrm wave reaches you. The best way to do this is to time the wyrm waves, which are about forty seconds apart (this is a rough estimate that is subject to correction), starting with one wyrm around 40-60 seconds. If you don't have a full charge, or you just don't think you'll live from the sheer number of wyrms, now is a good time to use a record piece. Grab one, and kill the mob of bluebladers (or what I like to call manhacks), to fill your charge. That, or hold jump until your bar is full. The right course of action is determined by how long it takes you to kill the manhacks. By now you know you can redirect wyrms via secondary shot, but with five bars of focus, it's much easier to hit more than one wyrm with a single blast. If they're close enough, the first blast actually deals enough damage to charge a second one, and then a third. Now, use your borrowed time to kill off the fodders, copters, and manhacks, while the wyrms slowly make their ways back to Savant. By now, a wyrm is often easy enough to kill via basic attack, but the situation varies.
To get the most charge back from each shot and the most damage output, it's better to shoot parallel into at least one wyrm, straight into its face. This also pushes the wyrm close to 180 degrees around, stalling it for longest.

Finally, and this is a personal preference, I've found it easier to tell which fodders are "aggro" by turning off GOTY mode. I've played on and off about equal amounts of time, and I started out on GOTY, so I have reason to believe others will find the same result.

With that, I conclude my humble advice. Good luck to you in your ascent! If you have anything to add or edit, again, tell me!

EDIT: Embarrassingly enough, I didn't notice that Q grabs records; thanks for pointing that out. UPDATE: I also found that using Q sometimes fails, and it has killed me on occasion. I think it's related to the spawning of wyrms, as they can also screw up your dodging.