I am dealing with the same issue right now... lots of keywords on the 2nd page of SERPs, and need to push them up to the 1st page. Only real answer is build links. Assuming of course that you've handled all your on-page technical SEO fixes, then link building is what's left.
Figure out where your competition is getting their links, see which ones you can also acquire, and go from there. High authority links, boom page 1.