Right at the beginning  of Chapter 24, you will have a lengthy fight on a large platform, which includes several Elephantaurs and a gaggle of Satyrs. After the fight, there will be a cutscene where you will see the arm come back into place, and once it ends, you'll notice a platform up and to your right that wasn't there before, and just beyond it is the entrance to this slide.

Important! There is an autosave after the fight, but the game also autosaves when you start the slide. This means that if you fail the slide, you cannot simply restart the checkpoint and get the trophy. Having said this, once the fight is over and autosave complete, it is recommended that you back up your save to the cloud or a USB drive before attempting the slide. Otherwise, failure will result in you having to do the entire fight over again just to get another chance at the trophy. 

It is best to watch a video demonstration a few times to get an idea for what to do.
 

Lubed Up - Video Guide

In Chapter 24 you have to repair the statue of Apollo. When you complete it's arm, you will have to proceed by sliding down te arm. Describing it would be difficult, so I suggest watching the video below a few times to get a feel for the course. Once you feel you are ready, give it a go. Know this, if you fail you have to start the entire chapter over again as a terribly placed autosave prevents you from getting the trophy should you fail and start again.
 

Lubed Up Trophy Guide