Trying to use and understand JSON API and get_posts

Me and my friend are breaking our heads to implement something. We are trying to get the results similar to function get_posts from JSON API (http://ift.tt/1Hddctm). The difference is: we want the columns from the table wp_posts where a cell from column post_type is equal our searches (the search is already implemented) and show that data in a JSON format. Example:

Search typed: attachment

Browser result: {"id":1, "page_author":1, "post_date_gmt":"2013-07-17 16:12:43", etc}

Just some light would be very helpful! We are using ajax to get what we want but it is not returning in JSON format like above =/