Difficult, difficult, lemon difficult...

Get work experience. It has to be the most effective route to making you employable, people want to employ people that can do the job and showing you have done some parts of the job before means you'll probably be able to to do it again.

You also get to be surrounded by people you aspire to be and in my experience most people are pretty keen on helping other people out. One stint of work experience can lead to others and don't be shy to ask. Don't ask, don't get. 

Everyone you work with will know other people and if they think you're competent and work hard they'll recommend you to others (it reflects well on them). Eventually, this can lead to job opporunities, you might even hear who is interviewing you what they are like and what they are sticklers for...

So if you can do anything in the next 12 months apart from doing well academically (that's obvious) it is to get some work experience and yes, you will get rejected and feel rubbish and you will get some really crap jobs but stick at it and put yourself in the right positions. It is up to, don't blame others for having all the connections, build your own - don't feel sorry for yourself and everyone who ever got anywhere had to work for it.