One question will this be your first law related work experience? If so it is often worth building up to mini-pupillage applications by having other legal experience on your CV, rather than instantly applying to a top ranked chambers in the field. It shows that you are being thoughtful and mature with your career choice, and also it can mean that you make the mistakes here rather than on the mini-pupillages themselves.
Try a few local solicitors firms for a one-week (unpaid) placement- just send your CV and covering letter. If you are lucky you may go to court and meet counsel, who in turn may give you a mini-pupillage. If not you can enthusiastically mention this legal experience and how you would now like to see the advocacy side of law in action on your next round of mini-pupillage applications.
As for mini-pupillages which chambers did you apply for? You really need a spread of both specialisations, and where the chambers are ranked (the Legal 500 is good for this). If let us say your four were: Matrix, Doughty Street, Blackstone, and 4-5 Gray's Inn I wouldn't get too downhearted; you really need a spread of applications ranging from not very well known criminal sets (that also deal in some HR work) to the leading Public law sets. Don't be afraid to apply for 8-10, it is inevitable that a number will turn you down, others that may wish to have you might not be able to accommodate you, and may ask for you to come back at Christmas, or even next year. For most chambers a CV and covering letter is enough- just keep on sending them out until you finally get something (of course tailoring the letter to each chambers using the relevant buzzwords from their websites).
The Bar is a career where almost everybody takes a few knocks getting into it- but perseverance is key.