The mini-game required for this achievement is found in the "Goodies" on the main menu screen (I am not clear on when you received this mini-game, but if you've played through the whole game, it is most likely there). This achievement and Nerves of Steel are gotten by completing this extremely long Slippery Floor game front to back.
You can die an infinite amount of times (and will die a lot, most likely).
You will receive Nerves of Steel for reaching the student at the "half-way" point. You receive a temporary checkpoint at the student's location, meaning if you fall off on the way back, you'll start again at his location. But if you exit to the main menu again, that checkpoint will be erased. So, if you are going to try to tackle these 2 achievements, it makes sense to do both at the same time.
These require 6+ mins of on-point d-pad usage in either direction -- the "stair" sequences being particularly challenging in terms of keeping your actions steady.
There are a few forks, you can search and reference a Youtube video to see the correct path, I take no credit for that or any pointers in this solution as I will not attempt it further after a good few deaths.