This applies to where I'm at in the USA - not sure about some other places.
Resume: Put the strongest areas first, in descending order. Education, experience, work history, skill set.
Apply for those jobs anyway, even if you don't meet all the criterea.
Apply for other jobs that are CLOSE, and have opportunities to advance to where you want to be.
Follow up! Don't pester them, but when they say they'll call you by Thursday - call them Friday morning if you haven't heard from them.
I went to college, but I never finished. I had zero "professional" programming experience - I had built some websites, and done some tech work for some small businesses, but essentially zero. I wasn't even looking for a programming job at the time, but I helped out a friend of a friend, we were talking ... and he was a manager in an IT department. He told me he could get me on - so I got him my resume as he said to do. I followed up - and it took months of it - and ended up getting a job as a Systems Analyst in the mortgage division of Regions.
He put me on some of the programmers "light work" so to speak. Other systems analytsts couldn't do it, and it let the experienced programmers focus on bigger things. I did systems integration programming, a lot of application / network / other troubleshooting for higher level people that couldn't wait on desktop support for - I was their "go to guy" for things like that. It was a thick client mortgage application that ran an entire copy with database on the laptops (there was no mobile internet back then, and they had to process applications in the field, at home, etc.) About a year later, I was moved into mortgage web systems as a programmer.
15 years later, I'm the lead programmer.
Take a leap. Be enthusiastic that "yes you can!" - but don't go so far that you're overpromising, or under delivering. I had used VB and .NET a little bit in college, but I wasn't really GOOD at it ... but I knew I could, so it went in my skill set (they used VB a lot there). Buddy up with an experienced programmer at work and you'll learn much more, much faster, and how things are done in the "real world" instead of contrived academic examples.