<form target="_blank" ...>
That's all that is needed.
But that doesn't open up the <form> in a new window!
That opens up the web page https://checkout.net/payment/CatalogPayment.aspx
in a new window.
If you want the <form> to open in a new window:
(a) it must be on its *OWN* web page and
(b) that has to happen via some action separate from the <form> page.