The trick is, in your application materials, to make it sound like your experience is equivalent to (or superior to) the experience they are asking for in the job posting. You need to get at the root of why they want that experience. E.g.: you may not have experience as a true field technician for HPLC/GC/MS, but if you are an expert in using this equipment over a period of seven years, and you have been in charge of troubleshooting problems with the equipment during that time as part of your position, this is what you'd want to highlight in your application(s). Don't apologize for not having field technician experience! Instead, state with confidence how your background is equivalent to what they want, and emphasize other intangibles (say, skill using your hands, a good problem solver, experience dealing with customers or interacting with other people, team player, etc.) that are also relevant - and point out why they would be relevant. This is where you want your cover letter to shine. Most recruiters recognize they won't find exactly what they are looking for. So they will take the closest thing to it that they can get.
PS - A headhunter can also help.