Connect to Windows Server 2012 with valid client certificate only?

With linux you can issue a certificate and put it into putty and disable password login.

I think this is a great way to stop pesky bots hammering RDP login the whole time.

I have noticed on the Start SSL website, they generate a certificate for you, which gets installed onto your browser and you don't need to type in a password to login, as long as you have that certificate in the browser.

Is it possible to connect to RDP using certificate authentication from the client?

Yes but you will need to install and configure your Remote Desktop Session host to use a Remote Desktop Gateway to do it.

Once you are using a Remote Desktop Gateway you can set up Remote Desktop Connection Authorization Policies (RD CAPs) and Desktop Resource Authorization Policies (RD RAPs) in those you can set things up like requiring that a connecting machine has a client certificate (per machine or per user).