Taking Advantage of Our Competitor's Weaknesses
Your strengths are your competitor's weaknesses. If not, they're not your strengths either. If they are, you could use them to his disadvantage.
For example: you have a strong financial position (and your competitor does not), you can bleed him out, through price war or excessive marketing.
In my opinion, however, you should not focus on eliminating the competition, but on creating value for your customer and having your competitor around to show to you are better.