How to turn a shiny metallic surface into a matte surface?

How do I turn a glossy/shiny surface into a non-shiny or matte surface in Adobe Photoshop?

I have here two images. The first is the image I would like to manipulate. The second image is the look I'm going for (not to replicate everything about it, but I want to achieve the same non-shiny look for the first image).

I'm aware that what I need to do is to dampen the highlights, and lower the contrast, but my attempts at adjusting the highlights via the Shadows/Highlights... menu and the contrast via the Brightness/Contrast... menu did not succeed. Adjusting colors by means of Replace Color... also did not yield success.

What other methods or techniques should I consider?