Have you tried adding support via register_cpt_onomy()?
I think you misunderstood me. I don’t need to register attachment post type as CTP-onomy. I need to assign CTP-onomy (let’s say CTP-onomy based on custom post type Games) to attachment post type.
It’s first option of your plugin: Attach to Post Types. It offers (in my case) Pages, Posts and custom post type Games. But what I need is to attach it to Attachment post type.
Nadia