On my first attempt at time attacking this level, I took pretty much the same path you see in this replay. I eliminated the prisons on the outside first, taking advantage of the conveyor belts and the huge amount of blue spheres to zip from one target to the next. There was barely anything I could use to go fast indoors, so it made sense.

When I looked at my time afterwards, I noticed I was less than a second off from getting the platinum. Turns out the platinum staff ghost started with the indoors prisons, so they couldn't carry speed accumulated outdoors like I did. The replay is of my second attempt.