you need link building pointing to your site with the keywords. Fresh content blog/articles/hubs/lens try all. Then you will find improvement.
Totally work in link building related work to stay in 1st page rank of any search engine first of all search engine submission, directory submission, Article submission, press release submission , forum posting, yahoo ans, social bookmarking.
Continues OffPage SEO works will keep you on the first page of the search engine. But important thing is that you have to use the fresh & informative content.
Just make sure that these low competition keywords are the most relevant for your website. They should be the exact words that your target market will most likely be using when searching for your products or services. There is no point going after low competition keywords if they are not targeted.
On page optimization is when you optimize the homepage and the internal pages of your website. On page SEO techniques include optimization of Page Title, Meta Tags, Meta Description, Content, etc. Off page optimization is when you promote your website and its pages. It is an outside technique. Off page optimization include directory submission, article submission, etc.