Those are some speedy boss times. :o
If you're wondering about Lava Shelter Hero, that being the one record I hold (I haven't really been bothered with the game much), then I myself do not get why I have that record. My technique is clearly not perfect, I never play that much at any game. And it isn't some secret route or anything... *shrug*
Learning that, unlike previous games, you can hold the direction while grinding and tapping the speed up button WITHOUT throwing yourself to your doom is handy because you can make some necessary rail jumps without needing lightning reactions.
Also generally, use the Light Dash. Oh it is so good.
Oh, and again on LS Hero, take the top route. Always. That's a general rule for most levels ever, but doesn't always work. The lower routes have far too much platform jumping, and that slows you down too much. Although for the top route you have to triangle jump at times, it's a small compromise.
</handing on of all the information I have to make me feel big>