Red modifies <em>tail</em>, not <em>pheasant</em> because the hikers spotted a pheasant with a red tail, not a red pheasant with a tail. When "a noun + an adjective" becomes a compound adjective, you need to use a hyphen.
Why is the headline of newspaper is important? The headline the hook of a story. That is, it's what catches your attention and gets you interested in the story.