Target companies that have the job you want, but also have the job you are currently qualified for. Get your foot in the door at your target company and work your way up to the job you really want. Focus on training and networking. It may take time but it would be worth it.
When your eye is on a different job be sure not to take your eye off your current job. Be great at what you currently do before you focus your efforts on your next step...you will get there faster.