Ctrl(cmd) + shift + alt + s ("Save for Web" window opens)
Choose the format you want.
If the file is still too large you also can play with quality:
Or Image size:
You also can check the layers in a tiff. And merge everything you can and check the doc size if you want to keep that format. If jpg works for you just save it "for web" ...
One of the problems with the example image is that it's a very noisy jpeg with with noticeable jpeg compression artifacts. It would be better to start with a RAW image file straight from the camera. The better the image quality is to begin with, the better the result will be.
Anyway, first thing I'd do is duplicate the image, turn it into a Smart Object, ...