How can I nail my interview for a HR role in a start up company?

If not, isn't it cheaper to outsource it to the recruitment agency?). This will show them that you really understand the business (if you do) and the kind of challenges they will have.

Hm, why would a start-up need an HR?
I mean, normally you would need a dedicated HR person if your company is at least 50-70 employees. Before that it's better to outsource key HR processes (recrutment, administration, training).
If the company is more than 50 FTE, then it's probably not a startup (it takes 3-5 years to grow business to such a size).
So I would try to sell myself by asking challenging questions - basically whether they should have an HR(e.g. "Why do you want to have an in-house recruitment? are you planning a constant pipeline of 15 positions at all times? If not, isn't it cheaper to outsource it to the recruitment agency?). This will show them that you really understand the business (if you do) and the kind of challenges they will have.