Welcome to another difficult achievement that is completed directly through muscle memory and memorization! Ok so if you're very good at platformers this shouldnt be too difficult, but at first it will seem impossible. This took me 4 attempts, and should take the average "platformer gamer" around 3-10 tries. The video at the bottom is a no death run from youtube and should be all you need, but i included some tips.
The first tip I have for this is on the section with the spiked balls going up and down where there are floating platforms. Jump on the platform and then jump kind of in place to land on the second colors platform. Now you will be high up and have plenty of time to fall and land on the next platform. ( im sorry if my explanations a bit off, re read when in the section practicing and it will make more sense lol)
On the color coded spike section where there are 4 colors, memorize where the spikes will land for each color. For example, red is the last spike, purple is the 3rd, etc.
Finally the hardest spot that will take the most practice is the section where you have to jump between colors (Around 10 minutes into video) The best tip I can give is to make sure to double jump when you can as opposed to using the upwards strike attack. This attack has landing lag making it difficult to recover from it. Always try to be one step ahead of the game. make sure to use the least time possible when jumping.
You will be aiming for the sub 20 minute run instead of 10 or less death side of the achievement. I ended this with 13 deaths in 19 minutes 45 seconds. LAST TIP:
Dont be afraid to do a practice run where you keep doing each area and dying at the end until you get it down 100 percent of the time or close. This will especially help in the color coded jumping section with the spikes.