After thinking about it, I would suggest this:
“Je lui tire mon chapeau”, “je vous tire mon chapeau” is the expression used when you personally want to say how impressedyou are by someone for doing something. It is used in conversation, to say, my hat off to you, Way to go! Kudos to you!

“Un coup de chapeau” conveys the same feeling, but I have seen it in articles, or mentions on the TV: “un grand coup de chapeau á Mr or Mme X for raising so much money for the Red Cross”. The author or anchor person is not speaking personally, but on behalf of a larger – not specially defined -group: a salute to what should be generally considered as an achievement.
You never hear “tu lui tires ton chapeau”. And you never hear “les Français lui tirent leur chapeau”. With the verb phrase, it is personal. Un coup de chapeau is exactly the same sentiment, but when you are not speaking for yourself. Some columns in newspapers would have the title: “coup de chapeau à…” : special kudos, salute to…

Of course, you can also personally say: “je pense que cette personne mérite un coup de chapeau”: you take your hat off to him/her and think others should do too!