when your keyword two competitive and it is two phrase , to avoid this competition you should find out some three phase which has traffic and optimize on that keywords gradually you can move on two phrase keyword.
For example you might decide you want to come up first for the term "insurance", but if you look at this term it's highly competitive. The sites that rank at the top for this keyword have 1000's of links, in order to rank well you would have to acquire a similar number of links, the average person is unlikely to be able to gather that many links. However if you tried ranking for "after the event insurance" you would do better because it's less competitive. "after the event insurance" is a long tail search term, the searcher has typed more words. Often when someone types this many words, they're looking for something in particular and if you satisfy their search with what they're looking for, you're very likely to get a conversion.
Just write unique useful content to your site and the search engines will be happy with that, your longtail traffic will start to show up, find other webmasters and buy links from them and your rankings will go up, also don't forget that it takes several months for the search engines to rank you so be patient.
This strategy is used particularly if your primary keywords is highly competitive. Long tail Keywords could be highly beneficial for you, because it targets more specific phrases.