honestly didn't even read the text besides the image before you replied, i thought that the "see rest" was just the remainder of the image and didn't bother
also the full explanation for my fast times have been stated multiple times previously, a glitch that lets you double jump without the upgrade lets the early levels go much faster by going through the saws, and although it is meaningless after stage 2 (assuming you got higher jump allowing you to go through the saws even without speed boosts), it makes those stages much faster. as for the build for both achievements, it's super jump x2 and speed x5 (the optimal build is speed x6 as i believe, but i keep fumbling it)
and the rest is me just goofing with myself