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Checkout form, how can I get this working?

So I am trying to setup a custom checkout form, I couldn’t find a way on how I can build this with the default tools provided maybe it is possible? if so do let me know how. Is there any third party services/utilities I can use to help create this or would I need to get a custom checkout form developed and then integrated and or embedded on to the site?

Here is the UI design links for the checkout page I am trying to create: