Build back links AND also revise web pages, update meta tags and make sure you have keyword rich contents.
As you See we all agree that to stay #1 at google you need to add Quality and related backlinks and also Fresh related content to your keyword. Good luck
Make the site updation regular and try to add as many possible keywords with each posts as possible and don't make it spam like for keywords so you should get better ranking. Also consistancy really matter. My site was on page 2 and now its on page 1 since a month.