This just doesn't look like it can be done safely. It looks like it's about 15 meters tall (diagonally), and the brush is thick enough to prevent you from just staying low down near the water. A fall from this height could easily result in serious injury or death.
Soccer cleats or trekking poles will not help here. They will be no more stable than the underlying dirt, which looks like loose, chossy gravel.
You could try to do it using mountaineering techniques, roping up and placing protection. However, the rock quality looks bad, and I don't see any cracks or other features that you could place protection in. You could try slinging trees and bushes, but from the photo that doesn't look like it will work.
If the rock quality of the cliffs is better than it looks, then conceivably you could drill and put in bolts, then do this traverse with a hand line or a belay. This would be a time-consuming and expensive project, would require permission from whoever controls the land, and would not be practical if you're talking about doing kilometers worth of traversing along this slope.
If you do decide to attempt it, wear helmets.