In the word press admin panel there is a category selection ‘helper panel’ which I am trying to recreate. However I can’t find the code for it, could someone point me in the right direction please?

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The actual Category Box that is created by WordPress is not typically used by Plugins that utilize a Custom UI. However, you can mimic its behavior, and you were most certainly on the right track with get_categories(). If you want to grab ALL categories, not just the ones with a post count, you need to call it like so:
‘hide_empty’ is what you were missing. Once you want to create your checkboxes, you would do something like this:
You can style the checkboxes however you like using a custom stylesheet, or you can apply the same tags and classes that the standard one uses, which will ensure that the existing WordPress Admin Stylesheet styles everything accordingly.