The idiom is "In The Public Eyes". It usually means 'Visible To All' and 'Known And Talked By So Many People'. For example, 1) Public figures constantly find themselves in the public eyes. [Meaning-1] 2) If we want support for improvements in our schools, we need to keep education in the public eyes. [Meaning-2]

The idiom is usually "in the public eye". It means to be well known to the public, usually because the person or thing in the public eye has been written or spoken about in the media. "The World Cup is very much in the public eye at this time." However, if you say "into the public eye", that emphasizes the process of becoming well known. "The recent epidemic of tuberculosis has brought that disease into to the public eye."